A166351 a(n) = (6*n)!/(3*n)!.

1, 120, 665280, 17643225600, 1295295050649600, 202843204931727360000, 58102407620643984998400000, 27500101936481280675682713600000, 20007974164906320568399715106816000000

Offset

0,2

Comments

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*(1/6)*exp(-(1/4)*x^(1/3))/(sqrt(Pi)*x^(5/6)), x=0..infinity), n=0,1... .

This solution is not unique.

Links

G. C. Greubel, Table of n, a(n) for n = 0..100

Formula

Asymptotics: a(n)=3*sqrt(2)*(1/3-1/(216*n)+1/(31104*n^2)+1003/(33592320*n^3)+ O(1/n^4))*(12^n)^3/(((1/n)^n)^3*(exp(n))^3), n->infinity.

Mathematica

Table[(6*n)!/(3*n)!, {n, 0, 25}] (* G. C. Greubel, May 10 2016 *)

Prog

(PARI) a(n) =(6*n)!/(3*n)!; \\ Michel Marcus, Aug 17 2013

Crossrefs

Sequence in context: A046987 A127232 A208191 * A147964 A172857 A308327

Adjacent sequences: A166348 A166349 A166350 * A166352 A166353 A166354

Keyword

nonn

Author

Karol A. Penson, Oct 12 2009

Status

approved