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A172492 a(n) = (n!)^2*(n+1)!. 2
1, 2, 24, 864, 69120, 10368000, 2612736000, 1024192512000, 589934886912000, 477847258398720000, 525631984238592000000, 763217641114435584000000, 1428743424166223413248000000, 3380406941577284595744768000000 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,changed
AUTHOR
Karol A. Penson, Feb 05 2010
STATUS
approved

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Last modified April 22 18:11 EDT 2024. Contains 371906 sequences. (Running on oeis4.)