A010795 a(n) = n!*(n+6)! / 6!.

1, 7, 112, 3024, 120960, 6652800, 479001600, 43589145600, 4881984307200, 659067881472000, 105450861035520000, 19719311013642240000, 4259371178946723840000, 1052064681199840788480000, 294578110735955420774400000, 92792104881825957543936000000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Delbert L. Johnson, Table of n, a(n) for n = 0..250
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A010791, A010792, A010793, A010794.

Programs

Maple

f := n->n!*(n+6)!/6!;

Mathematica

Table[n! * (n + 6)!/6!, {n, 0, 15}] (* Amiram Eldar, Sep 27 2022 *)

PARI

a(n)=n!^2*binomial(n+6,6) \\ Charles R Greathouse IV, Oct 23 2023

Formula

From Amiram Eldar, Sep 27 2022: (Start)

Sum_{n>=0} 1/a(n) = 720*BesselI(6,2).

Sum_{n>=0} (-1)^n/a(n) = 720*BesselJ(6,2). (End)

a(n) = 1/([x^n] hypergeom([], [7], x)).- Peter Luschny, Sep 13 2024