This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A000909 #27 May 04 2025 04:27:27
%S A000909 1,12,720,100800,25401600,10059033600,5753767219200,4487938430976000,
%T A000909 4577697199595520000,5914384781877411840000,9439358111876349296640000,
%U A000909 18236839872145106841108480000,41944731705933745734549504000000
%N A000909 a(n) = (2*n)!*(2*n+1)! / n!^2.
%C A000909 From _Karol A. Penson_, Jun 04 2009: (Start)
%C A000909 Integral representation of a(n) as n-th moment of a positive function W(x) = (1/4)*BesselK(1,(1/2)*sqrt(x))/Pi on the positive axis: a(n) = Integral_{x=0..oo} x^n*W(x) dx, n >= 0.
%C A000909 This is the solution of the Stieltjes moment problem with the moments a(n).
%C A000909 This solution may not be unique. (End)
%D A000909 E. R. Hansen, A Table of Series and Products, Prentice-Hall, Englewood Cliffs, NJ, 1975, p. 96.
%H A000909 T. D. Noe, <a href="/A000909/b000909.txt">Table of n, a(n) for n = 0..100</a>
%H A000909 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%t A000909 Table[(2*n)! (2*n+1)!/n!^2, {n, 0, 15}] (* _T. D. Noe_, Jun 20 2012 *)
%o A000909 (PARI) a(n)=binomial(2*n,n)*(2*n+1)! \\ _Charles R Greathouse IV_, Jan 12 2012
%Y A000909 a(n) = 4^n * A079484(n+1).
%K A000909 nonn,easy
%O A000909 0,2
%A A000909 _N. J. A. Sloane_