A172492 - OEIS

%I #11 Apr 22 2024 07:34:38

%S 1,2,24,864,69120,10368000,2612736000,1024192512000,589934886912000,

%T 477847258398720000,525631984238592000000,763217641114435584000000,

%U 1428743424166223413248000000,3380406941577284595744768000000

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

%C 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.

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

%F 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... .

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

%F This solution of the Stieltjes moment problem is not unique.

%o (Python)

%o from math import factorial

%o def A172492(n): return factorial(n)**3*(n+1) # _Chai Wah Wu_, Apr 22 2024

%K nonn

%O 0,2

%A _Karol A. Penson_, Feb 05 2010