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COMMENTS
| Integral representation as n-th moment of a positive function on a positive
halfaxis (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.
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FORMULA
| G.f.: sum(a(n)*x^n/(n!)^6,n=0..infinity)=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.
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