A172492 a(n) = (n!)^2*(n+1)!.

1, 2, 24, 864, 69120, 10368000, 2612736000, 1024192512000, 589934886912000, 477847258398720000, 525631984238592000000, 763217641114435584000000, 1428743424166223413248000000, 3380406941577284595744768000000

Offset

0,2

Comments

Asymptotics: a(n)->(1/16)*Pi^(3/2)*sqrt(2)*(32*n^2+40*n+9)*exp(-3*n)*(n)^(1/2+3*n), n->infinity.

Links

Table of n, a(n) for n=0..13.

Formula

Generating function of hypergeometric type, in Maple notation: sum(a(n)*x^n/(n!)^3, n=0..infinity)=1/(1-x)^2.

Integral representation as n-th moment of a positive function on a positive half-axis (solution of the Stieltjes moment problem), in Maple notation: a(n)=int(x^n*MeijerG([[],[]],[[0,0,1],[]],x),x=0..infinity), n=0,1... .

The MeijerG function above cannot be represented by any other known special function.

This solution of the Stieltjes moment problem is not unique.

Prog

(Python)
from math import factorial
def A172492(n): return factorial(n)**3*(n+1) # Chai Wah Wu, Apr 22 2024

Crossrefs

Sequence in context: A099704 A265879 A339946 * A322895 A264559 A012186

Adjacent sequences: A172489 A172490 A172491 * A172493 A172494 A172495

Keyword

nonn,changed

Author

Karol A. Penson, Feb 05 2010

Status

approved