Generating functions for Generalized Andrews-Euler sums With respect to the polynomial, 3 x + 2 + 5/x for all moduli from 2 to, 20 By Shalosh B. Ekhad Let A(m,j) be the coefficient of x^j in the expansion of m (3 x + 2 + 5/x) For a between 0 and k/2, let ----- \ b(m, a, k) = ) A(m, j) / ----- j where j goes over all integers (pos. or neg.) that are a mod k Let G[k,a](t) be the generating function of b(m,a,k) w.r.t. to m In other words: infinity ----- \ m G[k, a](t) = ) b(m, a, k) t / ----- m = 0 Then we have the following explicit expressions, as rational functions in , t k=, 2 G[2,0](t) = (-1+2*t)/(6*t+1)/(10*t-1) G[2,1](t) = -8*t/(6*t+1)/(10*t-1) k=, 3 G[3,0](t) = (11*t^2-1+4*t)/(10*t-1)/(7*t^2+4*t+1) G[3,1](t) = t*(-5+t)/(10*t-1)/(7*t^2+4*t+1) G[3,2](t) = -t*(19*t+3)/(10*t-1)/(7*t^2+4*t+1) k=, 4 G[4,0](t) = -(-1+2*t)*(-1+4*t+26*t^2)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1) G[4,1](t) = t*(-5+20*t+28*t^2)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1) G[4,2](t) = 34*t^2*(-1+2*t)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1) G[4,3](t) = -t*(92*t^2+3-12*t)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1) k=, 5 G[5,0](t) = -(-8*t+1-21*t^2+148*t^3+61*t^4)/(10*t-1)/(505*t^4+20*t^3-35*t^2+1) G[5,1](t) = -t*(-30*t+5-90*t^2+341*t^3)/(10*t-1)/(505*t^4+20*t^3-35*t^2+1) G[5,2](t) = t^2*(73*t-25+329*t^2)/(10*t-1)/(505*t^4+20*t^3-35*t^2+1) G[5,3](t) = t^2*(349*t^2-89*t-9)/(10*t-1)/(505*t^4+20*t^3-35*t^2+1) G[5,4](t) = -t*(781*t^3-54*t^2+3-18*t)/(10*t-1)/(505*t^4+20*t^3-35*t^2+1) k=, 6 G[6,0](t) = (-1+2*t)*(41*t^2+4*t-1)*(11*t^2-1+4*t)/(6*t+1)/(10*t-1)/(7*t^2+4*t+ 1)/(39*t^2-12*t+1) G[6,1](t) = -t*(-105*t^2+5-40*t+740*t^3+548*t^4)/(6*t+1)/(10*t-1)/(7*t^2+4*t+1) /(39*t^2-12*t+1) G[6,2](t) = -t^2*(-1+2*t)*(569*t^2+100*t-25)/(6*t+1)/(10*t-1)/(7*t^2+4*t+1)/(39 *t^2-12*t+1) G[6,3](t) = 152*t^3*(11*t^2-1+4*t)/(6*t+1)/(10*t-1)/(7*t^2+4*t+1)/(39*t^2-12*t+ 1) G[6,4](t) = t^2*(-1+2*t)*(391*t^2-36*t+9)/(6*t+1)/(10*t-1)/(7*t^2+4*t+1)/(39*t^ 2-12*t+1) G[6,5](t) = -t*(3308*t^4-63*t^2+444*t^3+3-24*t)/(6*t+1)/(10*t-1)/(7*t^2+4*t+1)/ (39*t^2-12*t+1) k=, 7 G[7,0](t) = -(-12*t+1+440*t^3-210*t^4-3192*t^5+889*t^6-15*t^2)/(10*t-1)/(5503*t ^6-72*t^5+1110*t^4+160*t^3-61*t^2-4*t+1) G[7,1](t) = t*(50*t-5+100*t^2-1400*t^3-175*t^4+3781*t^5)/(10*t-1)/(5503*t^6-72* t^5+1110*t^4+160*t^3-61*t^2-4*t+1) G[7,2](t) = -t^2*(-200*t+25-525*t^2+3943*t^3+1039*t^4)/(10*t-1)/(5503*t^6-72*t^ 5+1110*t^4+160*t^3-61*t^2-4*t+1) G[7,3](t) = -t^3*(-669*t+125-2574*t^2+5609*t^3)/(10*t-1)/(5503*t^6-72*t^5+1110* t^4+160*t^3-61*t^2-4*t+1) G[7,4](t) = t^3*(2986*t^2-27-463*t+5471*t^3)/(10*t-1)/(5503*t^6-72*t^5+1110*t^4 +160*t^3-61*t^2-4*t+1) G[7,5](t) = t^2*(5701*t^4+189*t^2-4457*t^3-9+72*t)/(10*t-1)/(5503*t^6-72*t^5+ 1110*t^4+160*t^3-61*t^2-4*t+1) G[7,6](t) = -t*(12919*t^5+105*t^4-60*t^2+840*t^3+3-30*t)/(10*t-1)/(5503*t^6-72* t^5+1110*t^4+160*t^3-61*t^2-4*t+1) k=, 8 G[8,0](t) = -(-1+2*t)*(-1+4*t+26*t^2)*(226*t^4+208*t^3-36*t^2-8*t+1)/(6*t+1)/( 10*t-1)/(8*t^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1) G[8,1](t) = -t*(2200*t^3+5-60*t-1050*t^4-15960*t^5+6632*t^6-75*t^2)/(6*t+1)/(10 *t-1)/(8*t^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1) G[8,2](t) = t^2*(-1+2*t)*(12004*t^4+5200*t^3-900*t^2-200*t+25)/(6*t+1)/(10*t-1) /(8*t^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1) G[8,3](t) = -t^3*(-2382*t^2+17528*t^3+125-1000*t+4952*t^4)/(6*t+1)/(10*t-1)/(8* t^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1) G[8,4](t) = -706*t^4*(-1+2*t)*(-1+4*t+26*t^2)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/( 932*t^4+208*t^3-36*t^2-8*t+1) G[8,5](t) = t^3*(-2558*t^2+216*t+8504*t^3+32728*t^4-27)/(6*t+1)/(10*t-1)/(8*t^2 -4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1) G[8,6](t) = t^2*(-1+2*t)*(19684*t^4+1872*t^3-324*t^2-72*t+9)/(6*t+1)/(10*t-1)/( 8*t^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1) G[8,7](t) = -t*(80792*t^6-630*t^4-9576*t^5-45*t^2+1320*t^3+3-36*t)/(6*t+1)/(10* t-1)/(8*t^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1) k=, 9 G[9,0](t) = (11*t^2-1+4*t)*(3349*t^6-5412*t^5+105*t^4+560*t^3-30*t^2-12*t+1)/( 10*t-1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1) G[9,1](t) = -t*(-70*t+5+3100*t^3-3950*t^4-34860*t^5+33740*t^6-30*t^2+65321*t^7) /(10*t-1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1) G[9,2](t) = -t^2*(-300*t+25+11000*t^3-5250*t^4-77613*t^5+17851*t^6-375*t^2)/(10 *t-1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1) G[9,3](t) = t^3*(11*t^2-1+4*t)*(10979*t^3-4125*t^2-750*t+125)/(10*t-1)/(7*t^2+4 *t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1) G[9,4](t) = -t^4*(-4757*t+625-14583*t^2+88126*t^3+50761*t^4)/(10*t-1)/(7*t^2+4* t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1) G[9,5](t) = -t^4*(-20451*t^2+2477*t-44262*t^3+167441*t^4+81)/(10*t-1)/(7*t^2+4* t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1) G[9,6](t) = t^3*(11*t^2-1+4*t)*(17839*t^3-891*t^2-162*t+27)/(10*t-1)/(7*t^2+4*t +1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1) G[9,7](t) = t^2*(148249*t^6-49397*t^5+135*t^2-3960*t^3+1890*t^4-9+108*t)/(10*t-\ 1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1) G[9,8](t) = -t*(425881*t^7+20244*t^6-2370*t^4-20916*t^5-18*t^2+1860*t^3+3-42*t) /(10*t-1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1) k=, 10 G[10,0](t) = (-1+2*t)*(841*t^4+268*t^3-51*t^2-8*t+1)*(-8*t+1-21*t^2+148*t^3+61* t^4)/(6*t+1)/(10*t-1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1) G[10,1](t) = t*(80*t-5-35*t^2-4060*t^3+9025*t^4+59960*t^5-119210*t^6-230680*t^7 +164512*t^8)/(6*t+1)/(10*t-1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35* t^2+1) G[10,2](t) = -t^2*(-1+2*t)*(140339*t^6+157800*t^5-8250*t^4-14000*t^3+750*t^2+ 300*t-25)/(6*t+1)/(10*t-1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2 +1) G[10,3](t) = -t^3*(-1500*t+125-1875*t^2+55000*t^3-24063*t^4-407748*t^5+87068*t^ 6)/(6*t+1)/(10*t-1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1) G[10,4](t) = t^4*(-1+2*t)*(262921*t^4+127084*t^3-21771*t^2-5000*t+625)/(6*t+1)/ (10*t-1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1) G[10,5](t) = -3368*t^5*(-8*t+1-21*t^2+148*t^3+61*t^4)/(6*t+1)/(10*t-1)/(281*t^4 +4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1) G[10,6](t) = -t^4*(-1+2*t)*(369719*t^4+45652*t^3-12709*t^2+648*t-81)/(6*t+1)/( 10*t-1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1) G[10,7](t) = t^3*(-27+324*t+405*t^2-11880*t^3-72455*t^4+398684*t^5+835372*t^6)/ (6*t+1)/(10*t-1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1) G[10,8](t) = t^2*(-1+2*t)*(337741*t^6-56808*t^5+2970*t^4+5040*t^3-270*t^2-108*t +9)/(6*t+1)/(10*t-1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1) G[10,9](t) = -t*(3-48*t+21*t^2+2436*t^3-5415*t^4-35976*t^5+71526*t^6+138408*t^7 +1842608*t^8)/(6*t+1)/(10*t-1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35 *t^2+1) k=, 11 G[11,0](t) = -(1-20*t+45*t^2+1200*t^3-5460*t^4-23184*t^5+122115*t^6+163560*t^7-\ 794025*t^8-333980*t^9+757789*t^10)/(10*t-1)/(4744279*t^10-359140*t^9+147775*t^8 +305920*t^7-14387*t^6-28304*t^5+1420*t^4+1000*t^3-65*t^2-12*t+1) G[11,1](t) = t*(-5+90*t-120*t^2-5040*t^3+16695*t^4+88410*t^5-298380*t^6-515160* t^7+1151655*t^8+453961*t^9)/(10*t-1)/(4744279*t^10-359140*t^9+147775*t^8+305920 *t^7-14387*t^6-28304*t^5+1420*t^4+1000*t^3-65*t^2-12*t+1) G[11,2](t) = t^2*(-25+400*t-175*t^2-20300*t^3+45125*t^4+299800*t^5-596050*t^6-\ 1173083*t^7+960341*t^8)/(10*t-1)/(4744279*t^10-359140*t^9+147775*t^8+305920*t^7 -14387*t^6-28304*t^5+1420*t^4+1000*t^3-65*t^2-12*t+1) G[11,3](t) = -t^3*(125-1750*t-750*t^2+77500*t^3-98750*t^4-864939*t^5+817256*t^6 +1396829*t^7)/(10*t-1)/(4744279*t^10-359140*t^9+147775*t^8+305920*t^7-14387*t^6 -28304*t^5+1420*t^4+1000*t^3-65*t^2-12*t+1) G[11,4](t) = -t^4*(625-7500*t-9375*t^2+277187*t^3-144372*t^4-2034366*t^5+669349 *t^6)/(10*t-1)/(4744279*t^10-359140*t^9+147775*t^8+305920*t^7-14387*t^6-28304*t ^5+1420*t^4+1000*t^3-65*t^2-12*t+1) G[11,5](t) = t^5*(-3125+30521*t+68332*t^2-859691*t^3-217267*t^4+2774281*t^5)/( 10*t-1)/(4744279*t^10-359140*t^9+147775*t^8+305920*t^7-14387*t^6-28304*t^5+1420 *t^4+1000*t^3-65*t^2-12*t+1) G[11,6](t) = -t^5*(243+13195*t-129860*t^2-260085*t^3+2321005*t^4+733939*t^5)/( 10*t-1)/(4744279*t^10-359140*t^9+147775*t^8+305920*t^7-14387*t^6-28304*t^5+1420 *t^4+1000*t^3-65*t^2-12*t+1) G[11,7](t) = -t^4*(81-972*t-1215*t^2+113765*t^3-485760*t^4-1664802*t^5+4134509* t^6)/(10*t-1)/(4744279*t^10-359140*t^9+147775*t^8+305920*t^7-14387*t^6-28304*t^ 5+1420*t^4+1000*t^3-65*t^2-12*t+1) G[11,8](t) = t^3*(378*t+162*t^2-16740*t^3+21330*t^4-202381*t^5+1380304*t^6-27+ 3979571*t^7)/(10*t-1)/(4744279*t^10-359140*t^9+147775*t^8+305920*t^7-14387*t^6-\ 28304*t^5+1420*t^4+1000*t^3-65*t^2-12*t+1) G[11,9](t) = t^2*(-7308*t^3+16245*t^4+107928*t^5-214578*t^6-9-2368349*t^7+144*t +4237801*t^8-63*t^2)/(10*t-1)/(4744279*t^10-359140*t^9+147775*t^8+305920*t^7-\ 14387*t^6-28304*t^5+1420*t^4+1000*t^3-65*t^2-12*t+1) G[11,10](t) = -t*(3-54*t+72*t^2+3024*t^3-10017*t^4-53046*t^5+179028*t^6+309096* t^7-690993*t^8+9457819*t^9)/(10*t-1)/(4744279*t^10-359140*t^9+147775*t^8+305920 *t^7-14387*t^6-28304*t^5+1420*t^4+1000*t^3-65*t^2-12*t+1) k=, 12 G[12,0](t) = -(-1+2*t)*(11*t^2-1+4*t)*(41*t^2+4*t-1)*(-1+4*t+26*t^2)*(t^4+208*t ^3-36*t^2-8*t+1)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(7*t^2+4*t+1)/(39*t^2-12*t+1)/( 2041*t^4+344*t^3-70*t^2-8*t+1) G[12,1](t) = -t*(5-100*t+6000*t^3-27300*t^4-115920*t^5+610575*t^6+225*t^2+ 817800*t^7-3970125*t^8-1669900*t^9+3966092*t^10)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1) /(7*t^2+4*t+1)/(39*t^2-12*t+1)/(2041*t^4+344*t^3-70*t^2-8*t+1) G[12,2](t) = t^2*(-1+2*t)*(1341574*t^8+3520400*t^7+472300*t^6-509800*t^5-33875* t^4+24800*t^3-200*t^2-400*t+25)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(7*t^2+4*t+1)/( 39*t^2-12*t+1)/(2041*t^4+344*t^3-70*t^2-8*t+1) G[12,3](t) = t^3*(11*t^2-1+4*t)*(438308*t^6-676500*t^5+13125*t^4+70000*t^3-3750 *t^2-1500*t+125)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(7*t^2+4*t+1)/(39*t^2-12*t+1)/( 2041*t^4+344*t^3-70*t^2-8*t+1) G[12,4](t) = -t^4*(-1+2*t)*(-1+4*t+26*t^2)*(147811*t^4+130000*t^3-22500*t^2-\ 5000*t+625)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(7*t^2+4*t+1)/(39*t^2-12*t+1)/(2041* t^4+344*t^3-70*t^2-8*t+1) G[12,5](t) = -t^5*(3125-37500*t+1357504*t^3-702177*t^4-9651324*t^5+2911532*t^6-\ 44688*t^2)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(7*t^2+4*t+1)/(39*t^2-12*t+1)/(2041*t ^4+344*t^3-70*t^2-8*t+1) G[12,6](t) = 16354*t^6*(-1+2*t)*(41*t^2+4*t-1)*(11*t^2-1+4*t)/(6*t+1)/(10*t-1)/ (8*t^2-4*t+1)/(7*t^2+4*t+1)/(39*t^2-12*t+1)/(2041*t^4+344*t^3-70*t^2-8*t+1) G[12,7](t) = -t^5*(243+74480*t^2-2916*t-518080*t^3-1691655*t^4+10786844*t^5+ 4981652*t^6)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(7*t^2+4*t+1)/(39*t^2-12*t+1)/(2041 *t^4+344*t^3-70*t^2-8*t+1) G[12,8](t) = -t^4*(-1+2*t)*(-1+4*t+26*t^2)*(408931*t^4+16848*t^3-2916*t^2-648*t +81)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(7*t^2+4*t+1)/(39*t^2-12*t+1)/(2041*t^4+344 *t^3-70*t^2-8*t+1) G[12,9](t) = t^3*(11*t^2-1+4*t)*(2043548*t^6-146124*t^5+2835*t^4+15120*t^3-810* t^2-324*t+27)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(7*t^2+4*t+1)/(39*t^2-12*t+1)/( 2041*t^4+344*t^3-70*t^2-8*t+1) G[12,10](t) = t^2*(-1+2*t)*(10227334*t^8+1267344*t^7+170028*t^6-183528*t^5-\ 12195*t^4+8928*t^3-72*t^2-144*t+9)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(7*t^2+4*t+1) /(39*t^2-12*t+1)/(2041*t^4+344*t^3-70*t^2-8*t+1) G[12,11](t) = -t*(3-60*t+135*t^2+3600*t^3-16380*t^4-69552*t^5+366345*t^6+490680 *t^7+51101492*t^10-2382075*t^8-1001940*t^9)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(7*t ^2+4*t+1)/(39*t^2-12*t+1)/(2041*t^4+344*t^3-70*t^2-8*t+1) k=, 13 G[13,0](t) = (24*t-1-99*t^2-1540*t^3+11655*t^4+28944*t^5-355236*t^6-95184*t^7+ 4217130*t^8-17373909*t^10-1287760*t^9+4728276*t^11+11413739*t^12)/(10*t-1)/( 120017353*t^12+26839596*t^11+5757339*t^10-6952960*t^9-1113818*t^8+985072*t^7+ 77884*t^6-58184*t^5-1115*t^4+1572*t^3-43*t^2-16*t+1) G[13,1](t) = -t*(-110*t+5+350*t^2+6900*t^3-41100*t^4-136920*t^5+1092840*t^6+ 922800*t^7-10081425*t^8-1457050*t^9+24403570*t^10+648701*t^11)/(10*t-1)/( 120017353*t^12+26839596*t^11+5757339*t^10-6952960*t^9-1113818*t^8+985072*t^7+ 77884*t^6-58184*t^5-1115*t^4+1572*t^3-43*t^2-16*t+1) G[13,2](t) = -t^2*(-500*t+25+1125*t^2+30000*t^3-136500*t^4-579600*t^5+3052875*t ^6+4089000*t^7-19850625*t^8-8172353*t^9+18590431*t^10)/(10*t-1)/(120017353*t^12 +26839596*t^11+5757339*t^10-6952960*t^9-1113818*t^8+985072*t^7+77884*t^6-58184* t^5-1115*t^4+1572*t^3-43*t^2-16*t+1) G[13,3](t) = t^3*(2250*t-125-3000*t^2-126000*t^3+417375*t^4+2210250*t^5-7459500 *t^6-12938049*t^7+29027571*t^8+13474789*t^9)/(10*t-1)/(120017353*t^12+26839596* t^11+5757339*t^10-6952960*t^9-1113818*t^8+985072*t^7+77884*t^6-58184*t^5-1115*t ^4+1572*t^3-43*t^2-16*t+1) G[13,4](t) = t^4*(10000*t-625-4375*t^2-507500*t^3+1128125*t^4+7475317*t^5-\ 14783152*t^6-28480706*t^7+22000859*t^8)/(10*t-1)/(120017353*t^12+26839596*t^11+ 5757339*t^10-6952960*t^9-1113818*t^8+985072*t^7+77884*t^6-58184*t^5-1115*t^4+ 1572*t^3-43*t^2-16*t+1) G[13,5](t) = -t^5*(-43750*t+3125-18750*t^2+1944061*t^3-2521238*t^4-21925281*t^5 +22058528*t^6+37125221*t^7)/(10*t-1)/(120017353*t^12+26839596*t^11+5757339*t^10 -6952960*t^9-1113818*t^8+985072*t^7+77884*t^6-58184*t^5-1115*t^4+1572*t^3-43*t^ 2-16*t+1) G[13,6](t) = -t^6*(-185313*t+15625-256245*t^2+6831260*t^3-2668890*t^4-49798455* t^5+11917951*t^6)/(10*t-1)/(120017353*t^12+26839596*t^11+5757339*t^10-6952960*t ^9-1113818*t^8+985072*t^7+77884*t^6-58184*t^5-1115*t^4+1572*t^3-43*t^2-16*t+1) G[13,7](t) = t^6*(792185*t^2-729-69377*t+1241740*t^3-21721910*t^4-407407*t^5+ 69820669*t^6)/(10*t-1)/(120017353*t^12+26839596*t^11+5757339*t^10-6952960*t^9-\ 1113818*t^8+985072*t^7+77884*t^6-58184*t^5-1115*t^4+1572*t^3-43*t^2-16*t+1) G[13,8](t) = -t^5*(-3402*t+243-3316970*t^4-1458*t^2+541285*t^3-9897321*t^5+ 59452264*t^6+26683861*t^7)/(10*t-1)/(120017353*t^12+26839596*t^11+5757339*t^10-\ 6952960*t^9-1113818*t^8+985072*t^7+77884*t^6-58184*t^5-1115*t^4+1572*t^3-43*t^2 -16*t+1) G[13,9](t) = -t^4*(-1296*t+65772*t^3+567*t^2-9787548*t^6-146205*t^4+981773*t^5+ 81-31419234*t^7+98578541*t^8)/(10*t-1)/(120017353*t^12+26839596*t^11+5757339*t^ 10-6952960*t^9-1113818*t^8+985072*t^7+77884*t^6-58184*t^5-1115*t^4+1572*t^3-43* t^2-16*t+1) G[13,10](t) = t^3*(-27216*t^3-27+477414*t^5+90153*t^4+45281437*t^8-1611252*t^6+ 486*t-12547489*t^7-648*t^2+110192129*t^9)/(10*t-1)/(120017353*t^12+26839596*t^ 11+5757339*t^10-6952960*t^9-1113818*t^8+985072*t^7+77884*t^6-58184*t^5-1115*t^4 +1572*t^3-43*t^2-16*t+1) G[13,11](t) = t^2*(180*t+208656*t^5-405*t^2-9-1472040*t^7-1099035*t^6+90836149* t^10+7146225*t^8-10800*t^3-45822305*t^9+49140*t^4)/(10*t-1)/(120017353*t^12+ 26839596*t^11+5757339*t^10-6952960*t^9-1113818*t^8+985072*t^7+77884*t^6-58184*t ^5-1115*t^4+1572*t^3-43*t^2-16*t+1) G[13,12](t) = -t*(-66*t+3+210*t^2+4140*t^3-24660*t^4-82152*t^5+655704*t^6+ 553680*t^7-6048855*t^8+14642142*t^10-874230*t^9+244210981*t^11)/(10*t-1)/( 120017353*t^12+26839596*t^11+5757339*t^10-6952960*t^9-1113818*t^8+985072*t^7+ 77884*t^6-58184*t^5-1115*t^4+1572*t^3-43*t^2-16*t+1) k=, 14 G[14,0](t) = -(-1+2*t)*(12641*t^6+9432*t^5-870*t^4-680*t^3+45*t^2+12*t-1)*(-12* t+1+440*t^3-210*t^4-3192*t^5+889*t^6-15*t^2)/(6*t+1)/(10*t-1)/(5503*t^6-72*t^5+ 1110*t^4+160*t^3-61*t^2-4*t+1)/(17599*t^6-1896*t^5-1546*t^4+176*t^3+99*t^2-20*t +1) G[14,1](t) = t*(120*t-5-7700*t^3+58275*t^4+144720*t^5-1776180*t^6-495*t^2-\ 475920*t^7+21085650*t^8-6438800*t^9-86869545*t^10+23641380*t^11+55474372*t^12)/ (6*t+1)/(10*t-1)/(5503*t^6-72*t^5+1110*t^4+160*t^3-61*t^2-4*t+1)/(17599*t^6-\ 1896*t^5-1546*t^4+176*t^3+99*t^2-20*t+1) G[14,2](t) = t^2*(-1+2*t)*(238291*t^10-61155500*t^9-26935125*t^8+11736000*t^7+ 3561000*t^6-951600*t^5-133500*t^4+36000*t^3+750*t^2-500*t+25)/(6*t+1)/(10*t-1)/ (5503*t^6-72*t^5+1110*t^4+160*t^3-61*t^2-4*t+1)/(17599*t^6-1896*t^5-1546*t^4+ 176*t^3+99*t^2-20*t+1) G[14,3](t) = -t^3*(-2500*t+125+150000*t^3-682500*t^4-2898000*t^5+15264375*t^6+ 5625*t^2+20445000*t^7-99075978*t^8-42456088*t^9+92775008*t^10)/(6*t+1)/(10*t-1) /(5503*t^6-72*t^5+1110*t^4+160*t^3-61*t^2-4*t+1)/(17599*t^6-1896*t^5-1546*t^4+ 176*t^3+99*t^2-20*t+1) G[14,4](t) = t^4*(-1+2*t)*(30527851*t^8+87773804*t^7+11866549*t^6-12745000*t^5-\ 846875*t^4+620000*t^3-5000*t^2-10000*t+625)/(6*t+1)/(10*t-1)/(5503*t^6-72*t^5+ 1110*t^4+160*t^3-61*t^2-4*t+1)/(17599*t^6-1896*t^5-1546*t^4+176*t^3+99*t^2-20*t +1) G[14,5](t) = t^5*(50000*t-3125-2537500*t^3+5620942*t^4+37632464*t^5-74092907*t^ 6-21875*t^2-147088084*t^7+113921212*t^8)/(6*t+1)/(10*t-1)/(5503*t^6-72*t^5+1110 *t^4+160*t^3-61*t^2-4*t+1)/(17599*t^6-1896*t^5-1546*t^4+176*t^3+99*t^2-20*t+1) G[14,6](t) = -t^6*(-1+2*t)*(88853489*t^6+97260312*t^5-4920054*t^4-8697512*t^3+ 462189*t^2+187500*t-15625)/(6*t+1)/(10*t-1)/(5503*t^6-72*t^5+1110*t^4+160*t^3-\ 61*t^2-4*t+1)/(17599*t^6-1896*t^5-1546*t^4+176*t^3+99*t^2-20*t+1) G[14,7](t) = -80312*t^7*(-12*t+1+440*t^3-210*t^4-3192*t^5+889*t^6-15*t^2)/(6*t+ 1)/(10*t-1)/(5503*t^6-72*t^5+1110*t^4+160*t^3-61*t^2-4*t+1)/(17599*t^6-1896*t^5 -1546*t^4+176*t^3+99*t^2-20*t+1) G[14,8](t) = t^6*(-1+2*t)*(171888271*t^6+76648552*t^5-13821930*t^4-2716760*t^3+ 368755*t^2-8748*t+729)/(6*t+1)/(10*t-1)/(5503*t^6-72*t^5+1110*t^4+160*t^3-61*t^ 2-4*t+1)/(17599*t^6-1896*t^5-1546*t^4+176*t^3+99*t^2-20*t+1) G[14,9](t) = -t^5*(243-3888*t+1701*t^2+1514510*t^4+197316*t^3-18539056*t^5-\ 35222019*t^6+300273548*t^7+110188748*t^8)/(6*t+1)/(10*t-1)/(5503*t^6-72*t^5+ 1110*t^4+160*t^3-61*t^2-4*t+1)/(17599*t^6-1896*t^5-1546*t^4+176*t^3+99*t^2-20*t +1) G[14,10](t) = -t^4*(-1+2*t)*(249750869*t^8+27656404*t^7-11295877*t^6+1651752*t^ 5+109755*t^4-80352*t^3+648*t^2+1296*t-81)/(6*t+1)/(10*t-1)/(5503*t^6-72*t^5+ 1110*t^4+160*t^3-61*t^2-4*t+1)/(17599*t^6-1896*t^5-1546*t^4+176*t^3+99*t^2-20*t +1) G[14,11](t) = t^3*(-27+540*t-1215*t^2-32400*t^3+147420*t^4+625968*t^5-3297105*t ^6-27389450*t^8-4416120*t^7+204329960*t^9+516649072*t^10)/(6*t+1)/(10*t-1)/( 5503*t^6-72*t^5+1110*t^4+160*t^3-61*t^2-4*t+1)/(17599*t^6-1896*t^5-1546*t^4+176 *t^3+99*t^2-20*t+1) G[14,12](t) = t^2*(-1+2*t)*(244035091*t^10-22015980*t^9-9696645*t^8+4224960*t^7 +1281960*t^6-342576*t^5-48060*t^4+12960*t^3+270*t^2-180*t+9)/(6*t+1)/(10*t-1)/( 5503*t^6-72*t^5+1110*t^4+160*t^3-61*t^2-4*t+1)/(17599*t^6-1896*t^5-1546*t^4+176 *t^3+99*t^2-20*t+1) G[14,13](t) = -t*(3-72*t+297*t^2+4620*t^3-34965*t^4-86832*t^5+1065708*t^6+ 285552*t^7-12651390*t^8+3863280*t^9+52121727*t^10-14184828*t^11+1186461908*t^12 )/(6*t+1)/(10*t-1)/(5503*t^6-72*t^5+1110*t^4+160*t^3-61*t^2-4*t+1)/(17599*t^6-\ 1896*t^5-1546*t^4+176*t^3+99*t^2-20*t+1) k=, 15 G[15,0](t) = -(11*t^2-1+4*t)*(-8*t+1-21*t^2+148*t^3+61*t^4)*(188159*t^8-161696* t^7-28792*t^6+26992*t^5+1130*t^4-1172*t^3+23*t^2+16*t-1)/(10*t-1)/(7*t^2+4*t+1) /(505*t^4+20*t^3-35*t^2+1)/(889921*t^8-508352*t^7+176856*t^6+3784*t^5-10926*t^4 +1132*t^3+119*t^2-24*t+1) G[15,1](t) = -t*(5-130*t+660*t^2+8360*t^3-78925*t^4-131670*t^5+2682120*t^6-\ 1022640*t^7-38430090*t^8+225213320*t^10+34768100*t^9-175524720*t^11-375839485*t ^12+117161459*t^13)/(10*t-1)/(7*t^2+4*t+1)/(505*t^4+20*t^3-35*t^2+1)/(889921*t^ 8-508352*t^7+176856*t^6+3784*t^5-10926*t^4+1132*t^3+119*t^2-24*t+1) G[15,2](t) = t^2*(600*t-25-2475*t^2-38500*t^3+291375*t^4+723600*t^5-8880900*t^6 -2379600*t^7+105428250*t^8-32194000*t^9-434347725*t^10+116612577*t^11+288532121 *t^12)/(10*t-1)/(7*t^2+4*t+1)/(505*t^4+20*t^3-35*t^2+1)/(889921*t^8-508352*t^7+ 176856*t^6+3784*t^5-10926*t^4+1132*t^3+119*t^2-24*t+1) G[15,3](t) = t^3*(11*t^2-1+4*t)*(264941*t^9-55365750*t^8+23420250*t^7+9362625*t ^6-3372750*t^5-406125*t^4+152250*t^3+1125*t^2-2250*t+125)/(10*t-1)/(7*t^2+4*t+1 )/(505*t^4+20*t^3-35*t^2+1)/(889921*t^8-508352*t^7+176856*t^6+3784*t^5-10926*t^ 4+1132*t^3+119*t^2-24*t+1) G[15,4](t) = -t^4*(-12500*t+625+28125*t^2+750000*t^3-3412500*t^4-14490000*t^5+ 76321875*t^6+102402147*t^7-497328507*t^8-211926146*t^9+482829769*t^10)/(10*t-1) /(7*t^2+4*t+1)/(505*t^4+20*t^3-35*t^2+1)/(889921*t^8-508352*t^7+176856*t^6+3784 *t^5-10926*t^4+1132*t^3+119*t^2-24*t+1) G[15,5](t) = t^5*(5197201*t^5-953125*t^4-1156250*t^3+109375*t^2+31250*t-3125)*( -8*t+1-21*t^2+148*t^3+61*t^4)/(10*t-1)/(7*t^2+4*t+1)/(505*t^4+20*t^3-35*t^2+1)/ (889921*t^8-508352*t^7+176856*t^6+3784*t^5-10926*t^4+1132*t^3+119*t^2-24*t+1) G[15,6](t) = t^6*(11*t^2-1+4*t)*(53942131*t^6-85212039*t^5+1522527*t^4+8769683* t^3-468750*t^2-187500*t+15625)/(10*t-1)/(7*t^2+4*t+1)/(505*t^4+20*t^3-35*t^2+1) /(889921*t^8-508352*t^7+176856*t^6+3784*t^5-10926*t^4+1132*t^3+119*t^2-24*t+1) G[15,7](t) = -t^7*(-1087189*t+78125-547482*t^2+48339085*t^3-58831910*t^4-\ 546065310*t^5+506244788*t^6+923957729*t^7)/(10*t-1)/(7*t^2+4*t+1)/(505*t^4+20*t ^3-35*t^2+1)/(889921*t^8-508352*t^7+176856*t^6+3784*t^5-10926*t^4+1132*t^3+119* t^2-24*t+1) G[15,8](t) = -t^7*(2187-4700622*t^2+360007*t-4503435*t^3+170147270*t^4-97279014 *t^5-1232117124*t^6+372967249*t^7)/(10*t-1)/(7*t^2+4*t+1)/(505*t^4+20*t^3-35*t^ 2+1)/(889921*t^8-508352*t^7+176856*t^6+3784*t^5-10926*t^4+1132*t^3+119*t^2-24*t +1) G[15,9](t) = t^6*(11*t^2-1+4*t)*(162597671*t^6-68398473*t^5-11642205*t^4+ 2361365*t^3-21870*t^2-8748*t+729)/(10*t-1)/(7*t^2+4*t+1)/(505*t^4+20*t^3-35*t^2 +1)/(889921*t^8-508352*t^7+176856*t^6+3784*t^5-10926*t^4+1132*t^3+119*t^2-24*t+ 1) G[15,10](t) = -t^5*(9356899*t^5+74115*t^4+89910*t^3-8505*t^2-2430*t+243)*(-8*t+ 1-21*t^2+148*t^3+61*t^4)/(10*t-1)/(7*t^2+4*t+1)/(505*t^4+20*t^3-35*t^2+1)/( 889921*t^8-508352*t^7+176856*t^6+3784*t^5-10926*t^4+1132*t^3+119*t^2-24*t+1) G[15,11](t) = -t^4*(81-1620*t+3645*t^2+97200*t^3-442260*t^4-1877904*t^5+9891315 *t^6-357284775*t^8+62076485*t^7-905958630*t^9+2600443409*t^10)/(10*t-1)/(7*t^2+ 4*t+1)/(505*t^4+20*t^3-35*t^2+1)/(889921*t^8-508352*t^7+176856*t^6+3784*t^5-\ 10926*t^4+1132*t^3+119*t^2-24*t+1) G[15,12](t) = t^3*(11*t^2-1+4*t)*(244083061*t^9-11959002*t^8+5058774*t^7+ 2022327*t^6-728514*t^5-87723*t^4+32886*t^3+243*t^2-486*t+27)/(10*t-1)/(7*t^2+4* t+1)/(505*t^4+20*t^3-35*t^2+1)/(889921*t^8-508352*t^7+176856*t^6+3784*t^5-10926 *t^4+1132*t^3+119*t^2-24*t+1) G[15,13](t) = t^2*(216*t-9-856656*t^7-11589840*t^9-891*t^2+37954170*t^8-13860*t ^3-156365181*t^10+104895*t^4-1178148641*t^11+260496*t^5+2544129901*t^12-3197124 *t^6)/(10*t-1)/(7*t^2+4*t+1)/(505*t^4+20*t^3-35*t^2+1)/(889921*t^8-508352*t^7+ 176856*t^6+3784*t^5-10926*t^4+1132*t^3+119*t^2-24*t+1) G[15,14](t) = -t*(3-78*t+396*t^2+5016*t^3-47355*t^4-79002*t^5+1609272*t^6-\ 613584*t^7+135127992*t^10-23058054*t^8+20860860*t^9-105314832*t^11-225503691*t^ 12+6170942719*t^13)/(10*t-1)/(7*t^2+4*t+1)/(505*t^4+20*t^3-35*t^2+1)/(889921*t^ 8-508352*t^7+176856*t^6+3784*t^5-10926*t^4+1132*t^3+119*t^2-24*t+1) k=, 16 G[16,0](t) = (-1+2*t)*(-1+4*t+26*t^2)*(226*t^4+208*t^3-36*t^2-8*t+1)*(50174*t^8 -94016*t^7-26992*t^6+18592*t^5+1580*t^4-992*t^3+8*t^2+16*t-1)/(6*t+1)/(10*t-1)/ (8*t^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1)/(347012*t^8+94016*t^7+26992*t^6-\ 18592*t^5-1580*t^4+992*t^3-8*t^2-16*t+1) G[16,1](t) = -t*(5-140*t+845*t^2+8840*t^3-103070*t^4-89320*t^5+3819585*t^6-\ 4216080*t^7-63027510*t^8+471961870*t^10+104489480*t^9-722533360*t^11-1327833220 *t^12+1218678160*t^13+645622352*t^14)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(932*t^4+ 208*t^3-36*t^2-8*t+1)/(347012*t^8+94016*t^7+26992*t^6-18592*t^5-1580*t^4+992*t^ 3-8*t^2-16*t+1) G[16,2](t) = -t^2*(-1+2*t)*(276163256*t^12-799125600*t^11-838374600*t^10+ 143846000*t^9+158843250*t^8-16653600*t^7-10883400*t^6+1263600*t^5+302625*t^4-\ 46000*t^3-2100*t^2+600*t-25)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(932*t^4+208*t^3-36 *t^2-8*t+1)/(347012*t^8+94016*t^7+26992*t^6-18592*t^5-1580*t^4+992*t^3-8*t^2-16 *t+1) G[16,3](t) = t^3*(-44404500*t^6-11898000*t^7+1456875*t^4+3618000*t^5-12375*t^2-\ 192500*t^3-125+3000*t+527141250*t^8-160970000*t^9-2173332948*t^10+597411792*t^ 11+1444254928*t^12)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+ 1)/(347012*t^8+94016*t^7+26992*t^6-18592*t^5-1580*t^4+992*t^3-8*t^2-16*t+1) G[16,4](t) = -t^4*(-1+2*t)*(-1+4*t+26*t^2)*(813316*t^8+58760000*t^7+16870000*t^ 6-11620000*t^5-987500*t^4+620000*t^3-5000*t^2-10000*t+625)/(6*t+1)/(10*t-1)/(8* t^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1)/(347012*t^8+94016*t^7+26992*t^6-18592 *t^5-1580*t^4+992*t^3-8*t^2-16*t+1) G[16,5](t) = -t^5*(381786522*t^6+509707824*t^7-17062500*t^4-72450000*t^5+140625 *t^2+3750000*t^3+3125-62500*t-2485048212*t^8-1017469744*t^9+2378896592*t^10)/(6 *t+1)/(10*t-1)/(8*t^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1)/(347012*t^8+94016*t ^7+26992*t^6-18592*t^5-1580*t^4+992*t^3-8*t^2-16*t+1) G[16,6](t) = t^6*(-1+2*t)*(828209224*t^8+2212532192*t^7+293061736*t^6-319097392 *t^5-21112826*t^4+15500000*t^3-125000*t^2-250000*t+15625)/(6*t+1)/(10*t-1)/(8*t ^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1)/(347012*t^8+94016*t^7+26992*t^6-18592* t^5-1580*t^4+992*t^3-8*t^2-16*t+1) G[16,7](t) = t^7*(-1858522820*t^6-3541546864*t^7+141310870*t^4+928214480*t^5-\ 566558*t^2-63201304*t^3-78125+1250000*t+2860548688*t^8)/(6*t+1)/(10*t-1)/(8*t^2 -4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1)/(347012*t^8+94016*t^7+26992*t^6-18592*t^ 5-1580*t^4+992*t^3-8*t^2-16*t+1) G[16,8](t) = -397186*t^8*(-1+2*t)*(-1+4*t+26*t^2)*(226*t^4+208*t^3-36*t^2-8*t+1 )/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1)/(347012*t^8+ 94016*t^7+26992*t^6-18592*t^5-1580*t^4+992*t^3-8*t^2-16*t+1) G[16,9](t) = -t^7*(2187-34992*t+1968434*t^2-33244410*t^4-21661656*t^3+833148496 *t^5-358013796*t^6-6133475568*t^7+1655761232*t^8)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1 )/(932*t^4+208*t^3-36*t^2-8*t+1)/(347012*t^8+94016*t^7+26992*t^6-18592*t^5-1580 *t^4+992*t^3-8*t^2-16*t+1) G[16,10](t) = t^6*(-1+2*t)*(4441695304*t^8+2133904864*t^7-337790232*t^6-\ 92990768*t^5+8777830*t^4+723168*t^3-5832*t^2-11664*t+729)/(6*t+1)/(10*t-1)/(8*t ^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1)/(347012*t^8+94016*t^7+26992*t^6-18592* t^5-1580*t^4+992*t^3-8*t^2-16*t+1) G[16,11](t) = -t^5*(243-4860*t+10935*t^2+291600*t^3-1326780*t^4-5633712*t^5+ 78502070*t^6-1218338700*t^8-350879920*t^7+7145405360*t^9+3162658352*t^10)/(6*t+ 1)/(10*t-1)/(8*t^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1)/(347012*t^8+94016*t^7+ 26992*t^6-18592*t^5-1580*t^4+992*t^3-8*t^2-16*t+1) G[16,12](t) = -t^4*(-1+2*t)*(244177156*t^8+7615296*t^7+2186352*t^6-1505952*t^5-\ 127980*t^4+80352*t^3-648*t^2-1296*t+81)*(-1+4*t+26*t^2)/(6*t+1)/(10*t-1)/(8*t^2 -4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1)/(347012*t^8+94016*t^7+26992*t^6-18592*t^ 5-1580*t^4+992*t^3-8*t^2-16*t+1) G[16,13](t) = t^3*(-27+648*t-2673*t^2-41580*t^3+314685*t^4+781488*t^5-9591372*t ^6+113862510*t^8-2569968*t^7-34769520*t^9-1689798668*t^10+5010475952*t^11+ 13735905328*t^12)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+1) /(347012*t^8+94016*t^7+26992*t^6-18592*t^5-1580*t^4+992*t^3-8*t^2-16*t+1) G[16,14](t) = t^2*(-1+2*t)*(6002374984*t^12+287685216*t^11+301814856*t^10-\ 51784560*t^9-57183570*t^8+5995296*t^7+3918024*t^6-454896*t^5-108945*t^4+16560*t ^3+756*t^2-216*t+9)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(932*t^4+208*t^3-36*t^2-8*t+ 1)/(347012*t^8+94016*t^7+26992*t^6-18592*t^5-1580*t^4+992*t^3-8*t^2-16*t+1) G[16,15](t) = -t*(3-84*t+507*t^2+5304*t^3-61842*t^4-53592*t^5+2291751*t^6-\ 2529648*t^7-37816506*t^8+62693688*t^9-433520016*t^11+283177122*t^10+731206896*t ^13-796699932*t^12+30896342192*t^14)/(6*t+1)/(10*t-1)/(8*t^2-4*t+1)/(932*t^4+ 208*t^3-36*t^2-8*t+1)/(347012*t^8+94016*t^7+26992*t^6-18592*t^5-1580*t^4+992*t^ 3-8*t^2-16*t+1) k=, 17 G[17,0](t) = (-1+32*t-255*t^2-1820*t^3+32305*t^4-24024*t^5-1349062*t^6+3780920* t^7+26472105*t^8-99755920*t^9-258615742*t^10+1086837864*t^11+1192887430*t^12-\ 4773429680*t^13-2146915380*t^14+5778283088*t^15+714530639*t^16)/(10*t-1)/( 74395018657*t^16+8654203952*t^15+5776961020*t^14-638889280*t^13-2092596542*t^12 +196322072*t^11+327569602*t^10-30049720*t^9-24203105*t^8+2579976*t^7+900754*t^6 -118416*t^5-15245*t^4+2700*t^3+49*t^2-24*t+1) G[17,1](t) = t*(-5+150*t-1050*t^2-9100*t^3+130650*t^4+8580*t^5-5182100*t^6+ 9880200*t^7+94827150*t^8-839434260*t^10-245884100*t^9+2187978600*t^11+ 3260966300*t^12-6507215400*t^13-3831509400*t^14+2905177519*t^15)/(10*t-1)/( 74395018657*t^16+8654203952*t^15+5776961020*t^14-638889280*t^13-2092596542*t^12 +196322072*t^11+327569602*t^10-30049720*t^9-24203105*t^8+2579976*t^7+900754*t^6 -118416*t^5-15245*t^4+2700*t^3+49*t^2-24*t+1) G[17,2](t) = -t^2*(25-700*t+4225*t^2+44200*t^3-515350*t^4-446600*t^5+19097925*t ^6-21080400*t^7-315137550*t^8+2359809350*t^10+522447400*t^9-3612666800*t^11-\ 6639166100*t^12+6107739707*t^13+3127669411*t^14)/(10*t-1)/(74395018657*t^16+ 8654203952*t^15+5776961020*t^14-638889280*t^13-2092596542*t^12+196322072*t^11+ 327569602*t^10-30049720*t^9-24203105*t^8+2579976*t^7+900754*t^6-118416*t^5-\ 15245*t^4+2700*t^3+49*t^2-24*t+1) G[17,3](t) = -t^3*(125-3250*t+16500*t^2+209000*t^3-1973125*t^4-3291750*t^5+ 67053000*t^6-25566000*t^7-960752250*t^8+5630333000*t^10+869202500*t^9-\ 4383335031*t^11-9415119001*t^12+2756849591*t^13)/(10*t-1)/(74395018657*t^16+ 8654203952*t^15+5776961020*t^14-638889280*t^13-2092596542*t^12+196322072*t^11+ 327569602*t^10-30049720*t^9-24203105*t^8+2579976*t^7+900754*t^6-118416*t^5-\ 15245*t^4+2700*t^3+49*t^2-24*t+1) G[17,4](t) = t^4*(-625+15000*t-962500*t^3-61875*t^2+7284375*t^4+18090000*t^5-\ 222022500*t^6-59490000*t^7+2635706250*t^8-806444323*t^9-10849127187*t^10+ 2983870314*t^11+7050682079*t^12)/(10*t-1)/(74395018657*t^16+8654203952*t^15+ 5776961020*t^14-638889280*t^13-2092596542*t^12+196322072*t^11+327569602*t^10-\ 30049720*t^9-24203105*t^8+2579976*t^7+900754*t^6-118416*t^5-15245*t^4+2700*t^3+ 49*t^2-24*t+1) G[17,5](t) = -t^5*(3125-68750*t+4312500*t^3+218750*t^2-25687500*t^4-85575000*t^ 5+683025000*t^6+577281441*t^7-6305142153*t^8-921816511*t^9+15330884518*t^10+ 105705401*t^11)/(10*t-1)/(74395018657*t^16+8654203952*t^15+5776961020*t^14-\ 638889280*t^13-2092596542*t^12+196322072*t^11+327569602*t^10-30049720*t^9-\ 24203105*t^8+2579976*t^7+900754*t^6-118416*t^5-15245*t^4+2700*t^3+49*t^2-24*t+1 ) G[17,6](t) = -t^6*(15625-312500*t+18750000*t^3+703125*t^2-85312500*t^4-\ 362072853*t^5+1906275405*t^6+2552082060*t^7-12357039465*t^8-5212237355*t^9+ 11680666531*t^10)/(10*t-1)/(74395018657*t^16+8654203952*t^15+5776961020*t^14-\ 638889280*t^13-2092596542*t^12+196322072*t^11+327569602*t^10-30049720*t^9-\ 24203105*t^8+2579976*t^7+900754*t^6-118416*t^5-15245*t^4+2700*t^3+49*t^2-24*t+1 ) G[17,7](t) = t^7*(-78125+1406250*t-78809049*t^3-1875000*t^2+261567963*t^4+ 1382291985*t^5-4688169060*t^6-8036974710*t^7+18183093783*t^8+7963286689*t^9)/( 10*t-1)/(74395018657*t^16+8654203952*t^15+5776961020*t^14-638889280*t^13-\ 2092596542*t^12+196322072*t^11+327569602*t^10-30049720*t^9-24203105*t^8+2579976 *t^7+900754*t^6-118416*t^5-15245*t^4+2700*t^3+49*t^2-24*t+1) G[17,8](t) = t^8*(-390625+6230317*t-317069402*t^3-2458813*t^2+692874665*t^4+ 4699924570*t^5-9176051374*t^6-18154695884*t^7+14158919759*t^8)/(10*t-1)/( 74395018657*t^16+8654203952*t^15+5776961020*t^14-638889280*t^13-2092596542*t^12 +196322072*t^11+327569602*t^10-30049720*t^9-24203105*t^8+2579976*t^7+900754*t^6 -118416*t^5-15245*t^4+2700*t^3+49*t^2-24*t+1) G[17,9](t) = -t^8*(6561+1848149*t-27297823*t^2+1199094895*t^4-6391218*t^3-\ 1621648262*t^5-13460760138*t^6+13482385796*t^7+22711424321*t^8)/(10*t-1)/( 74395018657*t^16+8654203952*t^15+5776961020*t^14-638889280*t^13-2092596542*t^12 +196322072*t^11+327569602*t^10-30049720*t^9-24203105*t^8+2579976*t^7+900754*t^6 -118416*t^5-15245*t^4+2700*t^3+49*t^2-24*t+1) G[17,10](t) = -t^7*(2187-39366*t+52488*t^2+11970121*t^3-124489893*t^4+ 4427386412*t^6-185154909*t^5-1825450266*t^7-31675608897*t^8+8457250051*t^9)/(10 *t-1)/(74395018657*t^16+8654203952*t^15+5776961020*t^14-638889280*t^13-\ 2092596542*t^12+196322072*t^11+327569602*t^10-30049720*t^9-24203105*t^8+2579976 *t^7+900754*t^6-118416*t^5-15245*t^4+2700*t^3+49*t^2-24*t+1) G[17,11](t) = t^6*(-729+14580*t-32805*t^2-874800*t^3+3980340*t^4-31926989*t^5+ 399259415*t^6-13093030775*t^8+857327260*t^7-1465512955*t^9+43490540569*t^10)/( 10*t-1)/(74395018657*t^16+8654203952*t^15+5776961020*t^14-638889280*t^13-\ 2092596542*t^12+196322072*t^11+327569602*t^10-30049720*t^9-24203105*t^8+2579976 *t^7+900754*t^6-118416*t^5-15245*t^4+2700*t^3+49*t^2-24*t+1) G[17,12](t) = -t^5*(243-5346*t+17010*t^2+335340*t^3-1997460*t^4-6654312*t^5+ 53112024*t^6-2443082255*t^8+288988705*t^7-5197765755*t^9+37318826002*t^10+ 14898276961*t^11)/(10*t-1)/(74395018657*t^16+8654203952*t^15+5776961020*t^14-\ 638889280*t^13-2092596542*t^12+196322072*t^11+327569602*t^10-30049720*t^9-\ 24203105*t^8+2579976*t^7+900754*t^6-118416*t^5-15245*t^4+2700*t^3+49*t^2-24*t+1 ) G[17,13](t) = -t^4*(81-1944*t+8019*t^2+124740*t^3-944055*t^4-2344464*t^5+ 28774116*t^6-341587530*t^8+7709904*t^7+1325011685*t^9-5916932121*t^10-\ 22355646606*t^11+62552049641*t^12)/(10*t-1)/(74395018657*t^16+8654203952*t^15+ 5776961020*t^14-638889280*t^13-2092596542*t^12+196322072*t^11+327569602*t^10-\ 30049720*t^9-24203105*t^8+2579976*t^7+900754*t^6-118416*t^5-15245*t^4+2700*t^3+ 49*t^2-24*t+1) G[17,14](t) = t^3*(-27+702*t-3564*t^2-45144*t^3+426195*t^4+711018*t^5-14483448* t^6+207522486*t^8+5522256*t^7-187747740*t^9-1216151928*t^10-5155682137*t^11+ 26443595719*t^12+66531828029*t^13)/(10*t-1)/(74395018657*t^16+8654203952*t^15+ 5776961020*t^14-638889280*t^13-2092596542*t^12+196322072*t^11+327569602*t^10-\ 30049720*t^9-24203105*t^8+2579976*t^7+900754*t^6-118416*t^5-15245*t^4+2700*t^3+ 49*t^2-24*t+1) G[17,15](t) = t^2*(59898864049*t^14+252*t-6875253*t^6+7588944*t^7-188081064*t^9 -15912*t^3-849531366*t^10-1521*t^2+1300560048*t^11+160776*t^5+2390099796*t^12+ 185526*t^4-32711198813*t^13-9+113449518*t^8)/(10*t-1)/(74395018657*t^16+ 8654203952*t^15+5776961020*t^14-638889280*t^13-2092596542*t^12+196322072*t^11+ 327569602*t^10-30049720*t^9-24203105*t^8+2579976*t^7+900754*t^6-118416*t^5-\ 15245*t^4+2700*t^3+49*t^2-24*t+1) G[17,16](t) = -t*(3-90*t+630*t^2+5460*t^3-78390*t^4-5148*t^5+3109260*t^6-\ 5928120*t^7-56896290*t^8+147530460*t^9+503660556*t^10-1312787160*t^11-\ 1956579780*t^12+3904329240*t^13+2298905640*t^14+150818956081*t^15)/(10*t-1)/( 74395018657*t^16+8654203952*t^15+5776961020*t^14-638889280*t^13-2092596542*t^12 +196322072*t^11+327569602*t^10-30049720*t^9-24203105*t^8+2579976*t^7+900754*t^6 -118416*t^5-15245*t^4+2700*t^3+49*t^2-24*t+1) k=, 18 G[18,0](t) = -(-1+2*t)*(11*t^2-1+4*t)*(41*t^2+4*t-1)*(3349*t^6-5412*t^5+105*t^4 +560*t^3-30*t^2-12*t+1)*(3401*t^6+5412*t^5-105*t^4-560*t^3+30*t^2+12*t-1)/(6*t+ 1)/(10*t-1)/(39*t^2-12*t+1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-\ 30*t^2-12*t+1)/(7239*t^6-396*t^5+1017*t^4+408*t^3-30*t^2-12*t+1) G[18,1](t) = t*(-5+160*t-1275*t^2-9100*t^3+161525*t^4-120120*t^5-6745310*t^6+ 18904600*t^7+132360525*t^8-1293078710*t^10-498779600*t^9+5434189320*t^11+ 5964437150*t^12-23867148400*t^13-10734576900*t^14+28891415440*t^15+3443513032*t ^16)/(6*t+1)/(10*t-1)/(39*t^2-12*t+1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t^ 4+712*t^3-30*t^2-12*t+1)/(7239*t^6-396*t^5+1017*t^4+408*t^3-30*t^2-12*t+1) G[18,2](t) = t^2*(-1+2*t)*(7413607321*t^14-5893493200*t^13-19214785100*t^12-\ 1454976800*t^11+4742458100*t^10+272643400*t^9-478388550*t^8-2126400*t^7+ 23637300*t^6-1136600*t^5-546850*t^4+53200*t^3+3850*t^2-700*t+25)/(6*t+1)/(10*t-\ 1)/(39*t^2-12*t+1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12 *t+1)/(7239*t^6-396*t^5+1017*t^4+408*t^3-30*t^2-12*t+1) G[18,3](t) = -t^3*(11*t^2-1+4*t)*(1420363468*t^12+2248009500*t^11-3704832375*t^ 10-90545000*t^9+768763125*t^8-50305500*t^7-55063875*t^6+5868000*t^5+1541250*t^4 -230000*t^3-10500*t^2+3000*t-125)/(6*t+1)/(10*t-1)/(39*t^2-12*t+1)/(7*t^2+4*t+1 )/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1)/(7239*t^6-396*t^5+1017*t^ 4+408*t^3-30*t^2-12*t+1) G[18,4](t) = -t^4*(-1+2*t)*(7148012819*t^12-19959008124*t^11-20964147969*t^10+ 3596150000*t^9+3971081250*t^8-416340000*t^7-272085000*t^6+31590000*t^5+7565625* t^4-1150000*t^3-52500*t^2+15000*t-625)/(6*t+1)/(10*t-1)/(39*t^2-12*t+1)/(7*t^2+ 4*t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1)/(7239*t^6-396*t^5+ 1017*t^4+408*t^3-30*t^2-12*t+1) G[18,5](t) = t^5*(-3125+75000*t-309375*t^2-4812500*t^3+36421875*t^4+90450000*t^ 5-1110112500*t^6-297450000*t^7+13176936927*t^8-4011495416*t^9-54259984842*t^10+ 14539902696*t^11+35570680672*t^12)/(6*t+1)/(10*t-1)/(39*t^2-12*t+1)/(7*t^2+4*t+ 1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1)/(7239*t^6-396*t^5+1017*t ^4+408*t^3-30*t^2-12*t+1) G[18,6](t) = t^6*(-1+2*t)*(41*t^2+4*t-1)*(11*t^2-1+4*t)*(125191*t^6-84562500*t^ 5+1640625*t^4+8750000*t^3-468750*t^2-187500*t+15625)/(6*t+1)/(10*t-1)/(39*t^2-\ 12*t+1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1)/(7239 *t^6-396*t^5+1017*t^4+408*t^3-30*t^2-12*t+1) G[18,7](t) = -t^7*(78125-1562500*t+3515625*t^2+93750000*t^3-426385353*t^4-\ 1813375764*t^5+9537577170*t^6+12856069680*t^7-62070403995*t^8-26657640724*t^9+ 59359749308*t^10)/(6*t+1)/(10*t-1)/(39*t^2-12*t+1)/(7*t^2+4*t+1)/(32167*t^6-\ 10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1)/(7239*t^6-396*t^5+1017*t^4+408*t^3-30* t^2-12*t+1) G[18,8](t) = t^8*(-1+2*t)*(19692481201*t^8+54633532712*t^7+7399173670*t^6-\ 7932557560*t^5-531068345*t^4+386791412*t^3-3065951*t^2-6250000*t+390625)/(6*t+1 )/(10*t-1)/(39*t^2-12*t+1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-\ 30*t^2-12*t+1)/(7239*t^6-396*t^5+1017*t^4+408*t^3-30*t^2-12*t+1) G[18,9](t) = 1972808*t^9*(11*t^2-1+4*t)*(3349*t^6-5412*t^5+105*t^4+560*t^3-30*t ^2-12*t+1)/(6*t+1)/(10*t-1)/(39*t^2-12*t+1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-\ 807*t^4+712*t^3-30*t^2-12*t+1)/(7239*t^6-396*t^5+1017*t^4+408*t^3-30*t^2-12*t+1 ) G[18,10](t) = -t^8*(-1+2*t)*(57046226639*t^8+60716731224*t^7-3346606662*t^6-\ 5334958088*t^5+301858905*t^4+110678988*t^3-9713137*t^2+104976*t-6561)/(6*t+1)/( 10*t-1)/(39*t^2-12*t+1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t ^2-12*t+1)/(7239*t^6-396*t^5+1017*t^4+408*t^3-30*t^2-12*t+1) G[18,11](t) = -t^7*(2187-43740*t+98415*t^2+2624400*t^3+36887105*t^4-636640908*t ^5-465356370*t^6-11990438925*t^8+21842080720*t^7-156589789260*t^9+45065487668*t ^10)/(6*t+1)/(10*t-1)/(39*t^2-12*t+1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t^ 4+712*t^3-30*t^2-12*t+1)/(7239*t^6-396*t^5+1017*t^4+408*t^3-30*t^2-12*t+1) G[18,12](t) = t^6*(-1+2*t)*(11*t^2-1+4*t)*(41*t^2+4*t-1)*(244121671*t^6-3945348 *t^5+76545*t^4+408240*t^3-21870*t^2-8748*t+729)/(6*t+1)/(10*t-1)/(39*t^2-12*t+1 )/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1)/(7239*t^6-\ 396*t^5+1017*t^4+408*t^3-30*t^2-12*t+1) G[18,13](t) = -t^5*(243-5832*t+24057*t^2+374220*t^3-2832165*t^4-7033392*t^5+ 86322348*t^6+195940535*t^8+23129712*t^7-9452699320*t^9-21412905738*t^10+ 179515091432*t^11+71689352048*t^12)/(6*t+1)/(10*t-1)/(39*t^2-12*t+1)/(7*t^2+4*t +1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1)/(7239*t^6-396*t^5+1017* t^4+408*t^3-30*t^2-12*t+1) G[18,14](t) = -t^4*(-1+2*t)*(159601672019*t^12+21824895556*t^11-8819849329*t^10 +466061040*t^9+514652130*t^8-53957664*t^7-35262216*t^6+4094064*t^5+980505*t^4-\ 149040*t^3-6804*t^2+1944*t-81)/(6*t+1)/(10*t-1)/(39*t^2-12*t+1)/(7*t^2+4*t+1)/( 32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1)/(7239*t^6-396*t^5+1017*t^4+ 408*t^3-30*t^2-12*t+1) G[18,15](t) = t^3*(11*t^2-1+4*t)*(30207680252*t^12-485570052*t^11+800243793*t^ 10+19557720*t^9-166052835*t^8+10865988*t^7+11893797*t^6-1267488*t^5-332910*t^4+ 49680*t^3+2268*t^2-648*t+27)/(6*t+1)/(10*t-1)/(39*t^2-12*t+1)/(7*t^2+4*t+1)/( 32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1)/(7239*t^6-396*t^5+1017*t^4+ 408*t^3-30*t^2-12*t+1) G[18,16](t) = t^2*(-1+2*t)*(155241292441*t^14-2121657552*t^13-6917322636*t^12-\ 523791648*t^11+1707284916*t^10+98151624*t^9-172219878*t^8-765504*t^7+8509428*t^ 6-409176*t^5-196866*t^4+19152*t^3+1386*t^2-252*t+9)/(6*t+1)/(10*t-1)/(39*t^2-12 *t+1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t^4+712*t^3-30*t^2-12*t+1)/(7239*t ^6-396*t^5+1017*t^4+408*t^3-30*t^2-12*t+1) G[18,17](t) = -t*(3-96*t+765*t^2+5460*t^3-96915*t^4+72072*t^5+4047186*t^6-\ 11342760*t^7-79416315*t^8+299267760*t^9+775847226*t^10-3260513592*t^11-\ 3578662290*t^12+14320289040*t^13+6440746140*t^14-17334849264*t^15+760795861208* t^16)/(6*t+1)/(10*t-1)/(39*t^2-12*t+1)/(7*t^2+4*t+1)/(32167*t^6-10428*t^5-807*t ^4+712*t^3-30*t^2-12*t+1)/(7239*t^6-396*t^5+1017*t^4+408*t^3-30*t^2-12*t+1) k=, 19 G[19,0](t) = (-1-357*t^2+36*t-1632*t^3+46440*t^4-112224*t^5-2054871*t^6+ 10199592*t^7+41785887*t^8-307967660*t^9-375985467*t^10+733307316*t^12+ 4525231152*t^11-33100737264*t^13+7170014310*t^14+105961115088*t^15-26331296733* t^16-98252965644*t^17+9829508411*t^18)/(10*t-1)/(1936320159271*t^18+ 212308081908*t^17-72109509171*t^16-23887438848*t^15+47942785782*t^14+7518884016 *t^13-9730011732*t^12-773960616*t^11+997346337*t^10+20359924*t^9-56477863*t^8+ 1569776*t^7+1771913*t^6-123136*t^5-27544*t^4+3128*t^3+119*t^2-28*t+1) G[19,1](t) = -t*(5-170*t+1520*t^2+8800*t^3-195475*t^4+306670*t^5+8464820*t^6-\ 32266520*t^7-172282825*t^8+1717926760*t^10+911703650*t^9-11708608240*t^11-\ 7687572410*t^12+68615701700*t^13+11914774600*t^14-147968800240*t^15-3262463315* t^16+51756090479*t^17)/(10*t-1)/(1936320159271*t^18+212308081908*t^17-\ 72109509171*t^16-23887438848*t^15+47942785782*t^14+7518884016*t^13-9730011732*t ^12-773960616*t^11+997346337*t^10+20359924*t^9-56477863*t^8+1569776*t^7+1771913 *t^6-123136*t^5-27544*t^4+3128*t^3+119*t^2-28*t+1) G[19,2](t) = t^2*(-25+800*t-6375*t^2-45500*t^3+807625*t^4-600600*t^5-33726550*t ^6+94523000*t^7+661802625*t^8-6465393550*t^10-2493898000*t^9+27170946600*t^11+ 29822185750*t^12-119335742000*t^13-53672884500*t^14+144327937037*t^15+ 18121546301*t^16)/(10*t-1)/(1936320159271*t^18+212308081908*t^17-72109509171*t^ 16-23887438848*t^15+47942785782*t^14+7518884016*t^13-9730011732*t^12-773960616* t^11+997346337*t^10+20359924*t^9-56477863*t^8+1569776*t^7+1771913*t^6-123136*t^ 5-27544*t^4+3128*t^3+119*t^2-28*t+1) G[19,3](t) = t^3*(-125+3750*t-26250*t^2-227500*t^3+3266250*t^4+214500*t^5-\ 129552500*t^6+247005000*t^7+2370678750*t^8-20985856500*t^10-6147102500*t^9+ 54699465000*t^11+81524157500*t^12-162723431721*t^13-95615548116*t^14+ 74179119931*t^15)/(10*t-1)/(1936320159271*t^18+212308081908*t^17-72109509171*t^ 16-23887438848*t^15+47942785782*t^14+7518884016*t^13-9730011732*t^12-773960616* t^11+997346337*t^10+20359924*t^9-56477863*t^8+1569776*t^7+1771913*t^6-123136*t^ 5-27544*t^4+3128*t^3+119*t^2-28*t+1) G[19,4](t) = -t^4*(625-17500*t+105625*t^2+1105000*t^3-12883750*t^4-11165000*t^5 +477448125*t^6-527010000*t^7-7878438750*t^8+58995233750*t^10+13061185000*t^9-\ 90302321093*t^11-166065245942*t^12+152076489674*t^13+79655323789*t^14)/(10*t-1) /(1936320159271*t^18+212308081908*t^17-72109509171*t^16-23887438848*t^15+ 47942785782*t^14+7518884016*t^13-9730011732*t^12-773960616*t^11+997346337*t^10+ 20359924*t^9-56477863*t^8+1569776*t^7+1771913*t^6-123136*t^5-27544*t^4+3128*t^3 +119*t^2-28*t+1) G[19,5](t) = -t^5*(3125-81250*t+412500*t^2+5225000*t^3-49328125*t^4-82293750*t^ 5+1676325000*t^6-639150000*t^7-24018806250*t^8+140720061248*t^10+21734845469*t^ 9-109803392349*t^11-234191798713*t^12+70528317359*t^13)/(10*t-1)/(1936320159271 *t^18+212308081908*t^17-72109509171*t^16-23887438848*t^15+47942785782*t^14+ 7518884016*t^13-9730011732*t^12-773960616*t^11+997346337*t^10+20359924*t^9-\ 56477863*t^8+1569776*t^7+1771913*t^6-123136*t^5-27544*t^4+3128*t^3+119*t^2-28*t +1) G[19,6](t) = t^6*(-15625+375000*t-1546875*t^2-24062500*t^3+452250000*t^5+ 182109375*t^4-5550562500*t^6-1488844323*t^7+65908599480*t^8-20089363540*t^9-\ 271913738565*t^10+73823511195*t^11+179777751221*t^12)/(10*t-1)/(1936320159271*t ^18+212308081908*t^17-72109509171*t^16-23887438848*t^15+47942785782*t^14+ 7518884016*t^13-9730011732*t^12-773960616*t^11+997346337*t^10+20359924*t^9-\ 56477863*t^8+1569776*t^7+1771913*t^6-123136*t^5-27544*t^4+3128*t^3+119*t^2-28*t +1) G[19,7](t) = -t^7*(78125-1718750*t+5468750*t^2+107812500*t^3-2138843559*t^5-\ 642187500*t^4+17069247708*t^6+14410778385*t^7-157288431585*t^8-22878008860*t^9+ 379609421578*t^10+2304638549*t^11)/(10*t-1)/(1936320159271*t^18+212308081908*t^ 17-72109509171*t^16-23887438848*t^15+47942785782*t^14+7518884016*t^13-\ 9730011732*t^12-773960616*t^11+997346337*t^10+20359924*t^9-56477863*t^8+1569776 *t^7+1771913*t^6-123136*t^5-27544*t^4+3128*t^3+119*t^2-28*t+1) G[19,8](t) = -t^8*(390625-7812500*t+17578125*t^2+468927147*t^3-9057312882*t^5-\ 2135292558*t^4+47811003015*t^6+63750678870*t^7-311401084509*t^8-129265549544*t^ 9+298093159669*t^10)/(10*t-1)/(1936320159271*t^18+212308081908*t^17-72109509171 *t^16-23887438848*t^15+47942785782*t^14+7518884016*t^13-9730011732*t^12-\ 773960616*t^11+997346337*t^10+20359924*t^9-56477863*t^8+1569776*t^7+1771913*t^6 -123136*t^5-27544*t^4+3128*t^3+119*t^2-28*t+1) G[19,9](t) = t^9*(-1953125+35097201*t-45930216*t^2-1969163343*t^3+34641739695*t ^5+6473536587*t^4-115846571892*t^6-202642221258*t^7+447140949711*t^8+ 202569837361*t^9)/(10*t-1)/(1936320159271*t^18+212308081908*t^17-72109509171*t^ 16-23887438848*t^15+47942785782*t^14+7518884016*t^13-9730011732*t^12-773960616* t^11+997346337*t^10+20359924*t^9-56477863*t^8+1569776*t^7+1771913*t^6-123136*t^ 5-27544*t^4+3128*t^3+119*t^2-28*t+1) G[19,10](t) = t^9*(-19683-9411331*t+155777608*t^2-88199839*t^3-7863965963*t^4+ 115934772292*t^6+17974987931*t^5-234860010106*t^7-446013269927*t^8+361775374541 *t^9)/(10*t-1)/(1936320159271*t^18+212308081908*t^17-72109509171*t^16-\ 23887438848*t^15+47942785782*t^14+7518884016*t^13-9730011732*t^12-773960616*t^ 11+997346337*t^10+20359924*t^9-56477863*t^8+1569776*t^7+1771913*t^6-123136*t^5-\ 27544*t^4+3128*t^3+119*t^2-28*t+1) G[19,11](t) = -t^8*(6561-131220*t+295245*t^2+56701325*t^3-719416810*t^4-\ 445078974*t^5+31074634015*t^6-345639285525*t^8-37501101590*t^7+327300944720*t^9 +578799978629*t^10)/(10*t-1)/(1936320159271*t^18+212308081908*t^17-72109509171* t^16-23887438848*t^15+47942785782*t^14+7518884016*t^13-9730011732*t^12-\ 773960616*t^11+997346337*t^10+20359924*t^9-56477863*t^8+1569776*t^7+1771913*t^6 -123136*t^5-27544*t^4+3128*t^3+119*t^2-28*t+1) G[19,12](t) = -t^7*(2187-48114*t+153090*t^2+3018060*t^3-17977140*t^4+184251817* t^5-2451679284*t^6+103012259705*t^8-3258476655*t^7-51906844920*t^9-768622753482 *t^10+217092305149*t^11)/(10*t-1)/(1936320159271*t^18+212308081908*t^17-\ 72109509171*t^16-23887438848*t^15+47942785782*t^14+7518884016*t^13-9730011732*t ^12-773960616*t^11+997346337*t^10+20359924*t^9-56477863*t^8+1569776*t^7+1771913 *t^6-123136*t^5-27544*t^4+3128*t^3+119*t^2-28*t+1) G[19,13](t) = t^6*(-729+17496*t-72171*t^2-1122660*t^3+8496495*t^4+21100176*t^5-\ 258967044*t^6+15281319020*t^8-1290092261*t^7+23475285460*t^9-354462454661*t^10-\ 39277696171*t^11+1109394834481*t^12)/(10*t-1)/(1936320159271*t^18+212308081908* t^17-72109509171*t^16-23887438848*t^15+47942785782*t^14+7518884016*t^13-\ 9730011732*t^12-773960616*t^11+997346337*t^10+20359924*t^9-56477863*t^8+1569776 *t^7+1771913*t^6-123136*t^5-27544*t^4+3128*t^3+119*t^2-28*t+1) G[19,14](t) = -t^5*(243-6318*t+32076*t^2+406296*t^3-3835755*t^4-6399162*t^5+ 130351032*t^6-1867702374*t^8-49700304*t^7+7793245285*t^9-37882757648*t^10-\ 136704329517*t^11+885054513529*t^12+377776047739*t^13)/(10*t-1)/(1936320159271* t^18+212308081908*t^17-72109509171*t^16-23887438848*t^15+47942785782*t^14+ 7518884016*t^13-9730011732*t^12-773960616*t^11+997346337*t^10+20359924*t^9-\ 56477863*t^8+1569776*t^7+1771913*t^6-123136*t^5-27544*t^4+3128*t^3+119*t^2-28*t +1) G[19,15](t) = -t^4*(81-2268*t+13689*t^2+143208*t^3-1669734*t^4-1446984*t^5+ 61877277*t^6-1021045662*t^8-68300496*t^7+1692729576*t^9+7645782294*t^10+ 18812537693*t^11-204616366914*t^12-529573820058*t^13+1597140692309*t^14)/(10*t-\ 1)/(1936320159271*t^18+212308081908*t^17-72109509171*t^16-23887438848*t^15+ 47942785782*t^14+7518884016*t^13-9730011732*t^12-773960616*t^11+997346337*t^10+ 20359924*t^9-56477863*t^8+1569776*t^7+1771913*t^6-123136*t^5-27544*t^4+3128*t^3 +119*t^2-28*t+1) G[19,16](t) = t^3*(-27+810*t-5670*t^2-49140*t^3+705510*t^4+46332*t^5-27983340*t ^6+512066610*t^8+53353080*t^7-1327774140*t^9-4532945004*t^10+11815084440*t^11+ 17609218020*t^12-187726853785*t^13+589661411740*t^14+1694387207771*t^15)/(10*t-\ 1)/(1936320159271*t^18+212308081908*t^17-72109509171*t^16-23887438848*t^15+ 47942785782*t^14+7518884016*t^13-9730011732*t^12-773960616*t^11+997346337*t^10+ 20359924*t^9-56477863*t^8+1569776*t^7+1771913*t^6-123136*t^5-27544*t^4+3128*t^3 +119*t^2-28*t+1) G[19,17](t) = t^2*(288*t-2295*t^2-16380*t^3-9+290745*t^4+10735986870*t^12-\ 216216*t^5+9781540776*t^11-12141558*t^6-42960867120*t^13+34028280*t^7-\ 19322238420*t^14+238248945*t^8-710934905333*t^15-897803280*t^9+1532309682001*t^ 16-2327541678*t^10)/(10*t-1)/(1936320159271*t^18+212308081908*t^17-72109509171* t^16-23887438848*t^15+47942785782*t^14+7518884016*t^13-9730011732*t^12-\ 773960616*t^11+997346337*t^10+20359924*t^9-56477863*t^8+1569776*t^7+1771913*t^6 -123136*t^5-27544*t^4+3128*t^3+119*t^2-28*t+1) G[19,18](t) = -t*(3+912*t^2-102*t+5280*t^3-117285*t^4+184002*t^5+5078892*t^6-\ 19359912*t^7-103369695*t^8+547022190*t^9+1030756056*t^10-4612543446*t^12-\ 7025164944*t^11+41169421020*t^13+7148864760*t^14-88781280144*t^15-1957477989*t^ 16+3845518467619*t^17)/(10*t-1)/(1936320159271*t^18+212308081908*t^17-\ 72109509171*t^16-23887438848*t^15+47942785782*t^14+7518884016*t^13-9730011732*t ^12-773960616*t^11+997346337*t^10+20359924*t^9-56477863*t^8+1569776*t^7+1771913 *t^6-123136*t^5-27544*t^4+3128*t^3+119*t^2-28*t+1) k=, 20 G[20,0](t) = (-1+2*t)*(-1+4*t+26*t^2)*(841*t^4+268*t^3-51*t^2-8*t+1)*(-8*t+1-21 *t^2+148*t^3+61*t^4)*(50399*t^8-47216*t^7-35092*t^6+16792*t^5+1805*t^4-992*t^3+ 8*t^2+16*t-1)/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505 *t^4+20*t^3-35*t^2+1)/(1391881*t^8+567688*t^7-34098*t^6-45080*t^5+371*t^4+1400* t^3-42*t^2-16*t+1) G[20,1](t) = t*(-5+180*t-1785*t^2-8160*t^3+232200*t^4-561120*t^5-10274355*t^6+ 50997960*t^7+208929435*t^8-1879927335*t^10-1539838300*t^9+22626155760*t^11+ 3666536580*t^12+47985280588*t^18-165503686320*t^13+35850071550*t^14+ 529805575440*t^15-131656483665*t^16-491264828220*t^17)/(10*t-1)/(6*t+1)/(8*t^2-\ 4*t+1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+ 567688*t^7-34098*t^6-45080*t^5+371*t^4+1400*t^3-42*t^2-16*t+1) G[20,2](t) = -t^2*(-1+2*t)*(128034254486*t^16+56054679200*t^15-341894661000*t^ 14-141160394000*t^13+100959057250*t^12+31260597600*t^11-13641221800*t^10-\ 2525794000*t^9+1016362125*t^8+77474000*t^7-41929300*t^6+197400*t^5+865375*t^4-\ 56000*t^3-6000*t^2+800*t-25)/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/(281*t^4+4*t^3+61*t ^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+567688*t^7-34098*t^6-45080*t^ 5+371*t^4+1400*t^3-42*t^2-16*t+1) G[20,3](t) = t^3*(-125+4000*t-31875*t^2-227500*t^3+4038125*t^4-3003000*t^5-\ 168632750*t^6+472615000*t^7+3309013125*t^8-32326967750*t^10-12469490000*t^9+ 135854733000*t^11+149110928750*t^12-596678710000*t^13-268493562663*t^14+ 722801946652*t^15+90736871668*t^16)/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/(281*t^4+4*t ^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+567688*t^7-34098*t^6-\ 45080*t^5+371*t^4+1400*t^3-42*t^2-16*t+1) G[20,4](t) = t^4*(-1+2*t)*(-1+4*t+26*t^2)*(7044030779*t^12-6757140000*t^11-\ 17163615000*t^10+981650000*t^9+3748893750*t^8-276840000*t^7-273210000*t^6+ 29340000*t^5+7706250*t^4-1150000*t^3-52500*t^2+15000*t-625)/(10*t-1)/(6*t+1)/(8 *t^2-4*t+1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^ 8+567688*t^7-34098*t^6-45080*t^5+371*t^4+1400*t^3-42*t^2-16*t+1) G[20,5](t) = -t^5*(-8*t+1-21*t^2+148*t^3+61*t^4)*(6482314532*t^10-3206312500*t^ 9-3598921875*t^8+1073250000*t^7+466218750*t^6-110512500*t^5-17390625*t^4+ 4500000*t^3+93750*t^2-62500*t+3125)/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/(281*t^4+4*t ^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+567688*t^7-34098*t^6-\ 45080*t^5+371*t^4+1400*t^3-42*t^2-16*t+1) G[20,6](t) = -t^6*(-1+2*t)*(173434271606*t^12-500448357552*t^11-523811938116*t^ 10+89942013752*t^9+99272248281*t^8-10408500000*t^7-6802125000*t^6+789750000*t^5 +189140625*t^4-28750000*t^3-1312500*t^2+375000*t-15625)/(10*t-1)/(6*t+1)/(8*t^2 -4*t+1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+ 567688*t^7-34098*t^6-45080*t^5+371*t^4+1400*t^3-42*t^2-16*t+1) G[20,7](t) = t^7*(1875000*t-78125-7734375*t^2-120312500*t^3+910546875*t^4+ 2261250000*t^5-27754406823*t^6-7417118124*t^7+329487196095*t^8-101307752120*t^9 -1357001832795*t^10+374485641516*t^11+890281006228*t^12)/(10*t-1)/(6*t+1)/(8*t^ 2-4*t+1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+ 567688*t^7-34098*t^6-45080*t^5+371*t^4+1400*t^3-42*t^2-16*t+1) G[20,8](t) = -t^8*(-1+2*t)*(-1+4*t+26*t^2)*(296277541*t^8+36835539728*t^7+ 10524618124*t^6-7266751528*t^5-616656059*t^4+387500000*t^3-3125000*t^2-6250000* t+390625)/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4 +20*t^3-35*t^2+1)/(1391881*t^8+567688*t^7-34098*t^6-45080*t^5+371*t^4+1400*t^3-\ 42*t^2-16*t+1) G[20,9](t) = -t^9*(-39062500*t+1953125+88067772*t^2+2340915648*t^3-10662822471* t^4-45137406636*t^5+238186109040*t^6+317328778176*t^7-1546606539351*t^8-\ 644131833508*t^9+1473530722292*t^10)/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/(281*t^4+4* t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+567688*t^7-34098*t^6-\ 45080*t^5+371*t^4+1400*t^3-42*t^2-16*t+1) G[20,10](t) = 9824674*t^10*(-1+2*t)*(841*t^4+268*t^3-51*t^2-8*t+1)*(-8*t+1-21*t ^2+148*t^3+61*t^4)/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/(281*t^4+4*t^3+61*t^2-16*t+1) /(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+567688*t^7-34098*t^6-45080*t^5+371*t^4+ 1400*t^3-42*t^2-16*t+1) G[20,11](t) = t^9*(-19683+393660*t-49713860*t^2+757630400*t^3-234327695*t^4-\ 39192106828*t^5+85731176080*t^6-1148531362175*t^8+582327523520*t^7-\ 2246160646660*t^9+1783863735988*t^10)/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/(281*t^4+4 *t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+567688*t^7-34098*t^6 -45080*t^5+371*t^4+1400*t^3-42*t^2-16*t+1) G[20,12](t) = -t^8*(-1+2*t)*(-1+4*t+26*t^2)*(55178740261*t^8+51398088976*t^7-\ 8611967988*t^6-2075107112*t^5+233774245*t^4+6508512*t^3-52488*t^2-104976*t+6561 )/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-\ 35*t^2+1)/(1391881*t^8+567688*t^7-34098*t^6-45080*t^5+371*t^4+1400*t^3-42*t^2-\ 16*t+1) G[20,13](t) = -t^7*(2187-52488*t+216513*t^2+3367980*t^3-25489485*t^4-63300528*t ^5+1997604257*t^6-27533410185*t^8-14440270092*t^7+539925706120*t^9-218350917267 *t^10-3906825114612*t^11+1060243230932*t^12)/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/( 281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+567688*t^7-\ 34098*t^6-45080*t^5+371*t^4+1400*t^3-42*t^2-16*t+1) G[20,14](t) = t^6*(-1+2*t)*(2744493154954*t^12+1292833752496*t^11-195279559164* t^10-53022674360*t^9+1471646455*t^8+485618976*t^7+317359944*t^6-36846576*t^5-\ 8824545*t^4+1341360*t^3+61236*t^2-17496*t+729)/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/( 281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+567688*t^7-\ 34098*t^6-45080*t^5+371*t^4+1400*t^3-42*t^2-16*t+1) G[20,15](t) = -t^5*(-8*t+1-21*t^2+148*t^3+61*t^4)*(31020527132*t^10-249322860*t ^9-279852165*t^8+83455920*t^7+36253170*t^6-8593452*t^5-1352295*t^4+349920*t^3+ 7290*t^2-4860*t+243)/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/(281*t^4+4*t^3+61*t^2-16*t+ 1)/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+567688*t^7-34098*t^6-45080*t^5+371*t^ 4+1400*t^3-42*t^2-16*t+1) G[20,16](t) = -t^4*(-1+2*t)*(151669405381*t^12+875725344*t^11+2224404504*t^10-\ 127221840*t^9-485856630*t^8+35878464*t^7+35408016*t^6-3802464*t^5-998730*t^4+ 149040*t^3+6804*t^2-1944*t+81)*(-1+4*t+26*t^2)/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/( 281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+567688*t^7-\ 34098*t^6-45080*t^5+371*t^4+1400*t^3-42*t^2-16*t+1) G[20,17](t) = t^3*(-27+864*t-6885*t^2-49140*t^3+872235*t^4-648648*t^5-36424674* t^6+714746835*t^8+102084840*t^7-2693409840*t^9-6982625034*t^10+8411626311628*t^ 16+29344622328*t^11+32207960610*t^12-128882601360*t^13-820906168385*t^14+ 3207771455876*t^15)/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/(281*t^4+4*t^3+61*t^2-16*t+1 )/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+567688*t^7-34098*t^6-45080*t^5+371*t^4 +1400*t^3-42*t^2-16*t+1) G[20,18](t) = t^2*(-1+2*t)*(3768465462634*t^16-20179684512*t^15+123082077960*t^ 14+50817741840*t^13-36345260610*t^12-11253815136*t^11+4910839848*t^10+909285840 *t^9-365890365*t^8-27890640*t^7+15094548*t^6-71064*t^5-311535*t^4+20160*t^3+ 2160*t^2-288*t+9)/(10*t-1)/(6*t+1)/(8*t^2-4*t+1)/(281*t^4+4*t^3+61*t^2-16*t+1)/ (505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+567688*t^7-34098*t^6-45080*t^5+371*t^4+ 1400*t^3-42*t^2-16*t+1) G[20,19](t) = -t*(336672*t^5-108*t+294758896932*t^17+4896*t^3+1071*t^2+ 78993890199*t^16+99302211792*t^13-139320*t^4+6164613*t^6-2199921948*t^12-\ 125357661*t^8+923902980*t^9-21510042930*t^14+3-30598776*t^7+19043997802892*t^18 -13575693456*t^11-317883345264*t^15+1127956401*t^10)/(10*t-1)/(6*t+1)/(8*t^2-4* t+1)/(281*t^4+4*t^3+61*t^2-16*t+1)/(505*t^4+20*t^3-35*t^2+1)/(1391881*t^8+ 567688*t^7-34098*t^6-45080*t^5+371*t^4+1400*t^3-42*t^2-16*t+1) This ends this gripping article, that took, 2.301, secodns to generate