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%I #23 Apr 01 2017 04:51:04
%S 1,12,720,100800,25401600,10059033600,5753767219200,4487938430976000,
%T 4577697199595520000,5914384781877411840000,9439358111876349296640000,
%U 18236839872145106841108480000,41944731705933745734549504000000
%N a(n) = (2n)!(2n+1)! / n!^2.
%C From _Karol A. Penson_, Jun 04 2009: (Start)
%C Integral representation of a(n) as n-th moment of a positive function W(x) on the positive axis, in Maple notation: a(n)=int(x^n*W(x),x=0..infinity) = int(x^n*(1/4)*BesselK(1,(1/2)*sqrt(x))/Pi,x=0..infinity), n=0,1,... .
%C This is the solution of the Stieltjes moment problem with the moments a(n).
%C This solution may not be unique. (End)
%D E. R. Hansen, A Table of Series and Products, Prentice-Hall, Englewood Cliffs, NJ, 1975, p. 96.
%H T. D. Noe, <a href="/A000909/b000909.txt">Table of n, a(n) for n = 0..100</a>
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>
%t Table[(2*n)! (2*n+1)!/n!^2, {n, 0, 15}] (* _T. D. Noe_, Jun 20 2012 *)
%o (PARI) a(n)=binomial(2*n,n)*(2*n+1)! \\ _Charles R Greathouse IV_, Jan 12 2012
%Y a(n) = 4^n * A079484(n+1).
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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