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A166351 a(n) = (6*n)!/(3*n)!. 2
1, 120, 665280, 17643225600, 1295295050649600, 202843204931727360000, 58102407620643984998400000, 27500101936481280675682713600000, 20007974164906320568399715106816000000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 16 11:10 EDT 2019. Contains 327095 sequences. (Running on oeis4.)