| G.f.:sum(a(n)*x^n/(n!)^3,n=0..infinity)=
4*EllipticK((1/2)*sqrt(2-2*sqrt(1-8*x)))^2/Pi^2,
sum(a(n)*x^n/(n!)^4,n=0..infinity)=hypergeom([1/2,1/2,1/2],[1,1,1],8*x).
Asymptotics:a(n)=(2*sqrt(2)/((exp(-1/2))^3*(exp(1/2))^3)-(1/4)*sqrt(2)/
((exp(-1/2))^3*(exp(1/2))^3*n)+(1/64)*sqrt(2)/((exp(-1/2))^3*
(exp(1/2))^3*n^2)+O(1/n^3))*(2^n)^3/(((1/n)^n)^3*(exp(n))^3),n->infinity.
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*MeijerG([[],[]],[[ -1/2,-1/2,-1/2],[]],x/8)/(8*(Pi)^(3/2)),
x=0..infinity), n=0,1... .
This solution is not unique.
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