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%I #16 Sep 08 2022 08:45:48
%S 1,14400,442597478400,311283409572495360000,
%T 1677789268237349829381980160000,
%U 41145365786974742781838753372569600000000,3375889771315468222156818412294164248002560000000000
%N a(n) = (A166351(n))^2 = ((6*n)!/((3*n)!))^2.
%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)*BesselK(0,(1/2)*x^(1/6))/(x^(5/6)*Pi)), x=0..infinity), n=0,1... .
%C This solution is not unique.
%H G. C. Greubel, <a href="/A166371/b166371.txt">Table of n, a(n) for n = 0..50</a>
%F 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).
%F 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.
%t Table[((6*n)!/(3*n)!)^2, {n, 0, 10}] (* _G. C. Greubel_, May 10 2016 *)
%o (Magma) [(Factorial(6*n)/(Factorial(3*n)))^2: n in [0..20]]; // _Vincenzo Librandi_, May 11 2016
%Y Cf. A166351
%K nonn
%O 0,2
%A _Karol A. Penson_, Oct 13 2009
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