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)*BesselK(0,(1/2)*x^(1/6))/(x^(5/6)*Pi)), x=0..infinity), n=0,1... .
This solution is not unique.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..50
FORMULA
G.f.: Sum{n>=0} a(n)*x^n/(n!)^6 = hypergeom([1/6, 1/6, 1/2, 1/2, 5/6, 5/6], [1, 1, 1, 1, 1], 2985984*x).
Asymptotics: a(n) = (2-1/(18*n) + 1/(1296*n^2)+247/(699840*n^3) + O(1/n^4))*(12^n)^6/((exp(n))^6*((1/n)^n)^6), n->infinity.
MATHEMATICA
Table[((6*n)!/(3*n)!)^2, {n, 0, 10}] (* G. C. Greubel, May 10 2016 *)
PROG
(Magma) [(Factorial(6*n)/(Factorial(3*n)))^2: n in [0..20]]; // Vincenzo Librandi, May 11 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Oct 13 2009
STATUS
approved