A010792 a(n) = n!*(n+3)! / 3!.

1, 4, 40, 720, 20160, 806400, 43545600, 3048192000, 268240896000, 28970016768000, 3766102179840000, 579979735695360000, 104396352425164800000, 21714441304434278400000, 5168037030455358259200000, 1395369998222946729984000000, 424192479459775805915136000000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A010791, A010793, A010794, A010795, A261879.

Programs

Magma

[Factorial(n)*Factorial(n+3)/6: n in [0..20]]; // Vincenzo Librandi, Feb 25 2017

Maple

f := n->n!*(n+3)!/3!;

Mathematica

Table[n! (n + 3)! / 3!, {n, 0, 20}] (* Vincenzo Librandi, Feb 25 2017 *)

PARI

a(n) = n!^2*binomial(n+3,3) \\ Charles R Greathouse IV, Oct 23 2023

Formula

From Amiram Eldar, Sep 27 2022: (Start)

Sum_{n>=0} 1/a(n) = 6*BesselI(3,2) = 6*A261879.

Sum_{n>=0} (-1)^n/a(n) = 6*BesselJ(3,2). (End)

a(n) = 1/([x^n] hypergeom([], [4], x)). - Peter Luschny, Sep 13 2024

Extensions

More terms from Vincenzo Librandi, Feb 25 2017