A218503 q-factorial numbers 5!_q.

1, 120, 9765, 251680, 3043425, 22661496, 121226245, 510902400, 1799118945, 5507702200, 15072415941, 37630041120, 87029433985, 188664603960, 386925380325, 756298318336, 1417430759745, 2559798038520, 4472991338725, 7589075296800, 12538953723681

Offset: 0

Author

Arkadiusz Wesolowski, Oct 31 2012

Keywords

• easy
• nonn

Links

• Index entries for sequences related to factorial numbers
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

Cf. A069777, A069778, A069779.

Programs

Mathematica

Table[QFactorial[5, n], {n, 0, 20}]
Join[{1},With[{f=Times@@Table[Total[n^Range[0,i]],{i,4}]},Table[f,{n,20}]]] (* or *) LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{1,120,9765,251680,3043425,22661496,121226245,510902400,1799118945,5507702200,15072415941},30] (* Harvey P. Dale, Sep 04 2017 *)

Formula

a(n) = (n + 1)*(n^2 + n + 1)*(n^3 + n^2 + n + 1)*(n^4 + n^3 + n^2 + n + 1).

G.f.: (1 + x*(109 + x*(8500 + x*(150700 + x*(792550 + x*(1454134 + x*(978436 + 5*x*(45788 + x*(3053 + 33*x)))))))))/(1 - x)^11.