This is the story about the number of ways of rearanging

           r identical Russian Dolls , each with n atomic dolls, into

                 smaller Russian Dolls, for r between 1 and , 3

                         and for n  between 0 and , 50

         The enumerating sequence for the number of ways of breaking-up

             one Russian Doll with i atomic dolls for i between 0

                               and , 50, equals

[1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437,

    190899322, 1382958545, 10480142147, 82864869804, 682076806159,

    5832742205057, 51724158235372, 474869816156751, 4506715738447323,

    44152005855084346, 445958869294805289, 4638590332229999353,

    49631246523618756274, 545717047936059989389, 6160539404599934652455,

    71339801938860275191172, 846749014511809332450147,

    10293358946226376485095653, 128064670049908713818925644,

    1629595892846007606764728147, 21195039388640360462388656799,

    281600203019560266563340426570, 3819714729894818339975525681317,

    52868366208550447901945575624941, 746289892095625330523099540639146,

    10738823330774692832768857986425209, 157450588391204931289324344702531067,

    2351152507740617628200694077243788988,

    35742549198872617291353508656626642567,

    552950118797165484321714693280737767385,

    8701963427387055089023600531855797148876,

    139258505266263669602347053993654079693415,

    2265418219334494002928484444705392276158355,

    37450059502461511196505342096431510120174682,

    628919796303118415420210454071849537746015761,

    10726137154573358400342215518590002633917247281,

    185724268771078270438257767181908917499221852770]

                          Note that this rings a Bell!

         The enumerating sequence for the number of ways of breaking-up

      2, identical Russian Dolls each with i atomic dolls, for i between 0

                               and , 50, equals

[1, 1, 3, 16, 139, 1750, 29388, 624889, 16255738, 504717929, 18353177160,

    769917601384, 36803030137203, 1984024379014193, 119571835094300406,

    7995677265437541258, 589356399302126773920, 47609742627231823142029,

    4193665147256300117666879, 400955337829516224119020233,

    41440870423841872676870218747, 4613078815253638377178567045525,

    551224589596619641029265258483892, 70488258533854548533464751355991589,

    9619268896143072038027084071649273161,

    1397298288308179147004374808565909827960,

    215540661865853438629397658928556821839664,

    35229812206006411403189828401695173576283880,

    6089040829423883845156354912229971519681572453,

    1110765849582182875905698301527188654790346156352,

    213483284571130384382541175703342054133435651103357,

    43157396210486847292630425842248780433432136112468237,

    9162706924744267739289631524078828876202536479042744037,

    2040034714206501862558972371338286913353110222594939723770,

    475665536260798918923370912891006910451994014541405053461911,

    115999282155519776818270127536938125598335231437027496135739662,

    29550758216925530485959355396395393619312609071345268686677939946,

    7854896341551900509088461180814144404608487153797274233308168884653,

    2176185339153561297044992575706693629694838648648837987817423092082150,

    627746426785855964862085083228846056036591175346031638788560204131555379,

    188355088777053235564210932632173937765206682520370184173719397777819045512

    , 58731053075348235626976279565492149017422095648934827488939776838695381\

    610616, 19013734315983523948443033142357175625820551944436842495113627076\

    861756725258119, 63856643777668110168615179519482596051723008215230502500\

    99916799267555963718877429, 222295333669176363171033028824808391223373469\

    2787209340359301495519093734292914280978, 8014978377864841172849261420119\

    80343748410173370223209203321680529310734004621031785332, 299087914691426\
    615101228463633836333749263385366428855308705479546136028672736540022834\

    396, 11542776340770065833001081274060680372633383349961074329799407225390\

    2148456917205764817300753, 4604047653885928241876399326893375861297700619\

    6978993755043121573702978207919651970386730501579, 1896717621887061027873\
    974710677240113070511724315494883189544671432218053623474591328911112264\

    2615, 8065390718041939509801740325363854209319583625483648635768364865578\

    610207675762868314055866181070615]

         The enumerating sequence for the number of ways of breaking-up

      3, identical Russian Dolls each with i atomic dolls, for i between 0

                               and , 50, equals

[1, 1, 4, 39, 862, 35775, 2406208, 238773109, 32867762616, 6009498859909,

    1412846181645855, 416415343791239162, 150747204270574506888,

    65905473934553360340713, 34305461329980340135062217,

    21003556204331356488142290707, 14967168378184553824642693791437,

    12300048738479761332056940912516760, 11562922299901153933108328821908919589,

    12344842532274351817061459485660871960491,

    14871412832618363386251688387241898724086716,

    20097292123793983120231221784372224973893317582,

    30307477554336416465303630772399662287619806671618,

    50757830196974964016776982965917820821358348287460147,

    93991877301680818859996559563166128923466126010837453210,

    191673125213260935566539465190219840767037557849461144587036,

    428847828447417554400805776029169452934828837274460515546505185,

    1049121496251433076887519218582751415831174168766042126522819709271,

    2797350988934140872461504063561991588077268438475553594235249133654894,

    8105536268146020190538152169610330937318213887558273714851465810376387490,
    254526026188498131612213416996800870545538362226302490878961199081520916\

    98157, 863930332033376816617751765067028585994334507607744197856792298024\

    58034257291109, 316207838448806092203456452900812656931639486065839444313\

    046498486814262305728885756, 12451724983319922113892892603896798527998894\

    15375786771326831592661559583509707931277941, 526409220579988051965262118\

    7232565513707581741586944072853821189868797799120059306449225022, 2384416\
    020224760423202888504379954159134085936160017031400341011502255599587892\

    6892094499247211, 1154998753092243031982448917889489246497173680509408665\

    14525023357894012183298675198264583700384056, 597232108555027316740733654\
    597847884891799877701659410094578360209648165162903720493184026108207756\

    993, 32910113933868285824255491610250740838359232432832851551851728301140\

    37957906523442460505697501825265000824, 192948192201892771665322203383920\
    417460440219971357079810122895286865293608837147788765513373882293014777\

    86647, 120174620339700636197072226311212143145491283430260296669806045516\

    847590502274954093826077406321045246643087400963, 79398753404406011822033\
    934487484852102655096742794879681733767685452292808386563569202036492412\

    5136975897496591573774, 5557018451096020753510294750561425054939521336531\

    140136495714607195715961324388923057102166364325797160662725580491563908,
    411456218781710790740057441639635116102860327353493384142134968485843381\

    64882643527483972465854480333724681214520181920654983, 321893044116100968\
    141528125170182595975284314927662961492343641185632987363618634085652849\

    564830674847761437507765515854323780835, 26575572104059341962778073321135\
    629616274707878773969093858797036569561290296451006857464640253727623469\

    19894066642182492015313167127, 231279098852616292386534603419901429539687\
    309293080998222036849033029330742985529759771322054402876309632374321415\

    29230668734813952923367, 211930687772028034039174533279905164986120156172\
    095559784795791595161320241853936402568241697776876008026645363481869599\

    262481075611244505392, 20426592623383323781973324806958504131206106221568\
    099543666814044915530727937721821390487500013798198488963870385137092464\

    15941252840709964568151, 206872268462302803090518703424169954573387905609\
    881218082910908672854639886419170806773761345406185181927614444489437744\

    45126390436897600839192539159, 219932870025208414926591338593770503240911\
    296874293728902728617562806199676753276464249310802863015710098955530653\

    335761851017885320188591568655993874066]

                          this took, 112.639, seconds