%I #15 May 10 2016 20:55:53
%S 1,120,665280,17643225600,1295295050649600,202843204931727360000,
%T 58102407620643984998400000,27500101936481280675682713600000,
%U 20007974164906320568399715106816000000
%N a(n) = (6*n)!/(3*n)!.
%C Integral representation as n-th moment of a positive function on a positive half-axis (solution of the Stieltjes moment problem).
%C 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... .
%C This solution is not unique.
%H G. C. Greubel, <a href="/A166351/b166351.txt">Table of n, a(n) for n = 0..100</a>
%F 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.
%t Table[(6*n)!/(3*n)!, {n, 0, 25}] (* _G. C. Greubel_, May 10 2016 *)
%o (PARI) a(n) =(6*n)!/(3*n)!; \\ _Michel Marcus_, Aug 17 2013
%K nonn
%O 0,2
%A _Karol A. Penson_, Oct 12 2009