A287699 a(n) = (n!)^3 * [x^n] hypergeom([], [1, 1], x)^4.

1, 4, 52, 1192, 36628, 1297504, 50419096, 2099649808, 92239977748, 4225417349872, 200149545055552, 9743739840316288, 485293084757188504, 24641572224240907264, 1272101807179840322416, 66620238759427147324192, 3532989709864148362611988, 189447449844340069835395984

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

Recurrence: (n-1)^2*n^6*(4179357*n^8 - 78014664*n^7 + 632906379*n^6 - 2915042445*n^5 + 8338804227*n^4 - 15175362645*n^3 + 17163198021*n^2 - 11033807142*n + 3088189672)*a(n) = (n-1)^2*(321810489*n^14 - 6972560595*n^13 + 68195663613*n^12 - 398723185476*n^11 + 1556210780586*n^10 - 4290176939202*n^9 + 8625424194708*n^8 - 12878626068195*n^7 + 14401770594884*n^6 - 12054703508348*n^5 + 7464118767536*n^4 - 3324818312080*n^3 + 1009161337280*n^2 - 187078472000*n + 15996099840)*a(n-1) - (4292199639*n^16 - 114458657040*n^15 + 1414085794758*n^14 - 10748138802219*n^13 + 56276210317086*n^12 - 215315257854096*n^11 + 622952233195566*n^10 - 1390775235633963*n^9 + 2422273491685843*n^8 - 3303218468438722*n^7 + 3516261474581476*n^6 - 2891864865024712*n^5 + 1801769964078784*n^4 - 822311126185120*n^3 + 259313519840640*n^2 - 50491775044480*n + 4574054714880)*a(n-2) + (n-2)^2*(41455042083*n^14 - 1064012746797*n^13 + 12496613326470*n^12 - 88977496857795*n^11 + 428877145565253*n^10 - 1479691251840690*n^9 + 3766745840954286*n^8 - 7184451834695931*n^7 + 10314626748833734*n^6 - 11091478948669399*n^5 + 8794647685753046*n^4 - 4988208446505900*n^3 + 1914324172568200*n^2 - 445291128023840*n + 47406419692800)*a(n-3) + 8*(n-3)^3*(n-2)^2*(87060185667*n^11 - 1712183651451*n^10 + 14956429421367*n^9 - 76542540324894*n^8 + 254862421705026*n^7 - 579589444734966*n^6 + 918686062982112*n^5 - 1015496680681101*n^4 + 767926983449420*n^3 - 378895216669900*n^2 + 109953142874960*n - 14239574392960)*a(n-4) - 175616*(n-4)^3*(n-3)^3*(n-2)^2*(4179357*n^8 - 44579808*n^7 + 203825727*n^6 - 521868123*n^5 + 819229437*n^4 - 808911855*n^3 + 491820735*n^2 - 168723870*n + 25050760)*a(n-5). - Vaclav Kotesovec, Jul 05 2018

a(n) ~ 2^(6*n + 5) / (3^(3/2) * Pi^3 * n^3). - Vaclav Kotesovec, Jul 05 2018

Maple

A287699_list := proc(len) series(hypergeom([], [1, 1], x)^4, x, len);
seq((n!)^3*coeff(%, x, n), n=0..len-1) end: A287699_list(18);

Mathematica

Table[SeriesCoefficient[HypergeometricPFQ[{}, {1, 1}, x]^4, {x, 0, n}] n!^3, {n, 0, 17}]

Crossrefs

Row 4 of A287698.

Sequence in context: A354262 A377576 A144829 * A377630 A280571 A343429

Adjacent sequences: A287696 A287697 A287698 * A287700 A287701 A287702

Keyword

nonn

Author

Peter Luschny, May 31 2017

Status

approved