%I #30 Sep 13 2024 11:29:19

%S 1,5,60,1260,40320,1814400,108864000,8382528000,804722688000,

%T 94152554496000,13181357629440000,2174924008857600000,

%U 417585409700659200000,92286375543845683200000,23256166637049112166400000,6628007491558996967424000000

%N a(n) = n!*(n+4)! / 4!.

%H Delbert L. Johnson, <a href="/A010793/b010793.txt">Table of n, a(n) for n = 0..251</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.

%F From _Amiram Eldar_, Sep 27 2022: (Start)

%F Sum_{n>=0} 1/a(n) = 24*BesselI(4,2).

%F Sum_{n>=0} (-1)^n/a(n) = 24*BesselJ(4,2). (End)

%F a(n) = 1/([x^n] hypergeom([], [5], x)). - _Peter Luschny_, Sep 13 2024

%p f := n->n!*(n+4)!/4!;

%t Table[n! * (n + 4)!/24, {n, 0, 20}] (* _Amiram Eldar_, Sep 27 2022 *)

%o (PARI) a(n) = n!*(n+4)! / 4!; \\ _Michel Marcus_, Mar 30 2023

%Y Cf. A010791, A010792, A010794, A010795.

%K nonn

%O 0,2

%A _N. J. A. Sloane_