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
KEYWORD
nonn
AUTHOR
Karol A. Penson, Oct 12 2009
STATUS
approved