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

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

Offset: 0

Author

Karol A. Penson, Feb 05 2010

Keywords

• nonn

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.

Programs

Python

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

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.