The first, 30, terms of the enumerating sequence for n by n matrices with all the row-sums and column-sums equal to, 1 and the entries are non-negative integers <=, 1, equals [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000, 51090942171709440000, 1124000727777607680000, 25852016738884976640000, 620448401733239439360000, 15511210043330985984000000, 403291461126605635584000000, 10888869450418352160768000000, 304888344611713860501504000000, 8841761993739701954543616000000, 265252859812191058636308480000000] The first, 30, terms of the enumerating sequence for n by n matrices with all the row-sums and column-sums equal to, 2 and the entries are non-negative integers <=, 1, equals [0, 1, 6, 90, 2040, 67950, 3110940, 187530840, 14398171200, 1371785398200, 158815387962000, 21959547410077200, 3574340599104475200, 676508133623135814000, 147320988741542099484000, 36574751938491748341360000, 10268902998771351157327104000, 3237415247416050491577971184000, 1138803698046507486981918971040000, 444432474300844787327725684969440000, 191444614738150142122968847365532800000, 90603353941858763724138404780662907040000, 46910877820213078135470477423451986527040000, 26469954647580538562900534131293144696816000000, 16219731108853857300315707916224741121084288000000, 10757893602266599121028776985362838529366417200000000, 7700062574890552884684882594168179635086240086688000000, 5931042368721990891450990939103756934155911159479328000000, 4903540714753612409051302387882754496626260238802683520000000, 4340900521317070710970287328154790305789223227035166385120000000] The first, 30, terms of the enumerating sequence for n by n matrices with all the row-sums and column-sums equal to, 2 and the entries are non-negative integers <=, 2, equals [1, 3, 21, 282, 6210, 202410, 9135630, 545007960, 41514583320, 3930730108200, 452785322266200, 62347376347779600, 10112899541133589200, 1908371363842760216400, 414517594539154672566000, 102681435747106627787376000, 28772944645196614863048048000, 9055359650665478876752602576000, 3180421710272322693959227638192000, 1239478835770026698838614159977440000, 533252395391438018873200088469644640000, 252081447537135601618562725529257444320000, 130383002914395989243171450112555145979040000, 73500396649726353004992119083172037827383680000, 44998990285095319505569239986172126591065712000000, 29822126709945409367599245263101584768212928912000000, 21329669586208423543172024912687248468757159489136000000, 16418096330385701209841149634391588025361231887006752000000, 13565143329998357358637627263315896888735964627900180384000000, 12001514711790706002011718434346457316922436224855572169120000000] The first, 30, terms of the enumerating sequence for n by n matrices with all the row-sums and column-sums equal to, 3 and the entries are non-negative integers <=, 1, equals [0, 0, 1, 24, 2040, 297200, 68938800, 24046189440, 12025780892160, 8302816499443200, 7673688777463632000, 9254768770160124288000, 14255616537578735986867200, 27537152449960680597739468800, 65662040698002721810659005184000, 190637228506535883540302038364160000, 665825560532772251175492202972938240000, 2767806480542211571651550187279222472704000, 13564406360915457771720399143711430952267776000, 77705104689340239554388061645133412621507133440000, 516344916592465985916193132955634668149853314252800000, 3952235963968636235373920011837764082275323312165683200000, 34625865751056601786040939091232067925054065762034992087040000, 345216770035327687605585138615897466610184682080602693354127360000, 3895853457976677864867654321956818370072419601979789614154252288000000, 49522400455794179580272274423460997875494831300307832047532880691200000000, 705862350216147733268489640719768814435847229884328960929338869116108800\ 000000, 11233957698968897356370426894487157802018583847602368650341701891\ 184158834688000000, 19885850643061550215214352111480857287502285922382260\ 0561777840124945712964698112000000, 3900984140604043576114981345521436871\ 243170324129369314291839620429490882080140165120000000] The first, 30, terms of the enumerating sequence for n by n matrices with all the row-sums and column-sums equal to, 3 and the entries are non-negative integers <=, 2, equals [0, 2, 31, 1344, 111920, 16214000, 3758757240, 1310799454720, 655551508577280, 452647176631372800, 418399785559398720000, 504669505260741099417600, 777461035821119354357452800, 1501959201213688265322501427200, 3581747697361314888194118659328000, 10399802599734067654449949502668800000, 36325391788208256168108171542936027136000, 151012959794833573952000702864304916267008000, 740124214638509781619452285653436089931988992000, 4240097082839750268939673959948739290739286999040000, 28176437095246682690719292849405816750954162552832000000, 215678462669664838270309253118328022714330946422864609280000, 1889645809650296205919040315112932090160032762958371385507840000, 18840215395581791425172232253235449841901250294949476189769564160000, 212622572784968713080166186525858170035040928467521102273298038784000000, 270283769768624485745108796093898158998141983157364892592483755622400000\ 0000, 3852553877963879737294423618724511978052619477246275158764459745436\ 5523968000000, 6131559435856009845707462537837619118166453427366396356463\ 66711443744310165504000000, 108540278461255320891398632618200781475989896\ 21297275905794433274691856438180970496000000, 212926044211146154209151925\ 660903720168567456143492167174663253496391617255126524231680000000] The first, 30, terms of the enumerating sequence for n by n matrices with all the row-sums and column-sums equal to, 3 and the entries are non-negative integers <=, 3, equals [1, 4, 55, 2008, 153040, 20933840, 4662857360, 1579060246400, 772200774683520, 523853880779443200, 477360556805016931200, 569060910292172349004800, 868071731152923490921728000, 1663043727673392444887284377600, 3937477620391471128913917360384000, 11361490405233269088852351904641024000, 39467705844323372236824674031640375296000, 163283938767642016139942363441093164154880000, 796824180968200160537736864316564823259205632000, 4547339119236385743822415218802509535838329405440000, 30113233378328189753888919011461446581273069067632640000, 229779098535365272804235213380938986408330152494454210560000, 2007428014014105245680247242799387436136350988603059855360000000, 19962214641200446756517827683897641074721848304075669914001080320000, 224744798953246553559219239969083879697977407522785494184550924288000000, 285062836813126487955962112557072242735373314101544365480110062357708800\ 0000, 4054927936618608885874953509804086255409361531997762815526901194552\ 8164352000000, 6441462337009747477561158810416039442496672821135674261378\ 67855076244300759040000000, 113826122220435888057083402625570943460666603\ 62187535487856695827617162067264405504000000, 222930577618063108322746098\ 264671287622593548426467313611646428360767547595808828293120000000] The first, 30, terms of the enumerating sequence for n by n matrices with all the row-sums and column-sums equal to, 4 and the entries are non-negative integers <=, 1, equals [0, 0, 0, 1, 120, 67950, 68938800, 116963796250, 315031400802720, 1289144584143523800, 7722015017013984456000, 65599839591251908982712750, 769237071909157579108571190000, 12163525741347497524178307740904300, 254143667822686635850590661555095468000, 6892692735539278753058456514221737762215000, 238871596129285108315684789088803525762942560000, 10431401634793817906193873163767479249710797568200000, 566895242033460637461017821037429791182821015953495488000, 37911589613425952733393718264069147678877877626169022024515000, 3088496938678002662586223525004709655841715076755052999658886600000, 303690552732350971707102530203860843720388559383169781279410045221650000, 357421097188854268380546529171777511719323004220685935977995694925651220\ 00000, 499641367549255499484275577040722567562912751024779271005270698484\ 9712274603690000, 8237620367227362542451154440949060985260102153453881423\ 24323811975517152108569484000000, 159142443870974024030710826204043945552\ 150403030641813588117787767761159501552799347325000000, 35809621722993869\ 656865764612462375997122219539026487722339497668853584791853216395799211\ 800000000, 93330021111742804006758170017897030125273962856175101835023714\ 74304038560163898575834429176529343750000, 280284690189675114436812126325\ 723523191406909127130921642962913084766302236076760212541829257276102333\ 4000000, 9652393753222819435968153969285020061350810016074643033931556336\ 97649952158769389881223147888331342878830667500000] The first, 30, terms of the enumerating sequence for n by n matrices with all the row-sums and column-sums equal to, 4 and the entries are non-negative integers <=, 2, equals [0, 1, 21, 2371, 628080, 342829125, 344827336455, 589985590963930, 1614966163545077280, 6736902064011471514050, 41169485539316907099731250, 356683733303639928299266819050, 4261817244676586430350506540348800, 68591162695421478976169922385168949550, 1456977454148671437117047063826306284903250, 40125878309014654627871871114724921424759175000, 1410534154843375091631579262249625381715863040672000, 62416386405108898784015639346499310921653128044848287000, 3433868575366156277789311627688438924686864081982913523107000, 232273808505581071157606795985678847488890659685774558806222665000, 19123971620037389217245351073838385478801698745028528964449043286000000, 189911218101597598735406381805433750394621834953244371749061035179387941\ 5000, 2255805269783088509365863818169617857165281723435384986456047898339\ 34843076965000, 318068677678969264430169696264890454410948033870877139970\ 09777243115441257116309290000, 528648832302001207595789945757835309164749\ 8916530556852637160236107468485857300100716000000, 1029051309334562960702\ 642970684966850583100126271487153001085719353435061125046959904555281250\ 000, 23320470042464226868990850363924871098059395569482466843087945868244\ 3067580242190233146878315497250000, 6118757174568185919839582332852670169\ 8777876704165787673068186476673461726556488339735948418485135067250000, 1\ 849175963001057761582291133760041273485372770595033870194217985728507786\ 5325111482276989092542123390547736000000, 6406150210694308487289576197662\ 573231781516810306594939128612494482441148866368372670652927825039301686\ 849120273750000] The first, 30, terms of the enumerating sequence for n by n matrices with all the row-sums and column-sums equal to, 4 and the entries are non-negative integers <=, 3, equals [0, 3, 87, 8515, 1992760, 971853075, 887226868605, 1397573379100570, 3564687080800036800, 13994422270858878448950, 81142871841524279822631750, 671520101271652710399345719850, 7707138964962257026620598104320400, 119704970610709982789146127744897675250, 2463458386245672328679573808456268563099750, 65949164854460383682147934685440527008344135000, 2259925433455165029125145653361384480536094064128000, 97722742113891689017833237752797952050105077009222957000, 5264842358301085710645446581101617989536025952411935327185000, 349386504852546133438847462576945313875421034231833558901433865000, 28267555012591270746544222048919368689431333995768282943187921508200000, 276236641636575317797254853646473734868120697189495263372485702204692854\ 5000, 3232941637444226902519968677266948946112870474872873747785931584450\ 43145484455000, 449642223329411825450014219897202683014672713081650915073\ 42729311234515936973958250000, 737896707932304469083286734833035291378846\ 4205515907208907992586524803428441334403512000000, 1419497480307160356368\ 252052527531363885991144726431564175809835919464724117436624904232293750\ 000, 31816497215536096235429753818656752519639060539341535476025484331066\ 5762386759976071793511928329750000, 8262470595972001026541074558024193433\ 7633820176259456840636743983373147524977994561089343737260240275250000, 2\ 473096268020708344216722693579778868643644254218233903197909920240710827\ 6359064372067843495122121709193330000000, 8490519678068698132011895192337\ 939738507840109752600255548831735549844562342011489955208523750514276946\ 907765126250000] The first, 30, terms of the enumerating sequence for n by n matrices with all the row-sums and column-sums equal to, 4 and the entries are non-negative integers <=, 4, equals [1, 5, 120, 10147, 2224955, 1047649905, 936670590450, 1455918295922650, 3680232136895819610, 14356628851597700179050, 82857993930808028192521800, 683327637694741065563262206250, 7821620120684573354895941635688250, 121226756408657335034315697817193707350, 2490562784819660349490404693413463514984500, 66583272259816204746406627604055923436126087000, 2279076203511044757135748751897740210364955533895000, 98458055431151530456778147600581220200521886860097275000, 5300252805595736035313032397806523176642462976789946788304000, 351499515037067154764556950151761640777013401021265237589794665000, 28422099859443904031778975820409617947237359065424797516070806534065000, 277608527526070501496957096985357249504529664476079933381230865434177567\ 5000, 3247590809194397422995244177820479165056627137019668744183591178719\ 38870863150000, 451508613190553007318860086995100229979611350214917643800\ 49777857964962911997452330000, 740712799901679812584849832161581629284808\ 2041644359324122568614371228428046058082622250000, 1424495173872394040096\ 533962461169904370899534956686000903368221430888039039857180897784322250\ 000, 31920160632132528182672625541023351962044532443683550011360313905136\ 3946437557679374386706370755000000, 8287455342045278474322292089854390726\ 6828545772217049336814489168647646505220053049645053129361941251250000, 2\ 480055506181824901751631859311430037589685692780932623167749422689110303\ 5005173013146279020320928163534133250000, 8512808845293483948648205758997\ 715386770463384131933810372748294531050549737351422270201482953299585297\ 525258398750000] The whole thing took, 262.380, seconds of CPU time