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 A166334 #21 May 02 2025 04:33:10
%S A166334 1,3,90,7560,1247400,340540200,138940401600,79196028912000,
%T A166334 60109785944208000,58607041295602800000,71383376298044210400000,
%U A166334 106218463931489785075200000,189599958117709266359232000000
%N A166334 a(n) = (3*n)!/(2^n*n!).
%C A166334 Integral representation as n-th moment of a positive function on a positive halfaxis (solution of the Stieltjes moment problem): a(n) = Integral_{x=0..oo} x^n*(1/3)*sqrt(2)*BesselK(1/3,(2/9)*sqrt(6*x))/(sqrt(x)*Pi) dx, n >= 0.
%C A166334 This solution is unique.
%H A166334 G. C. Greubel, <a href="/A166334/b166334.txt">Table of n, a(n) for n = 0..100</a>
%F A166334 G.f.: Sum_{n>=0} a(n)*x^n/(n!)^2 = hypergeom([1/3, 2/3], [1], (27/2)*x).
%F A166334 Asymptotics: a(n)=(sqrt(3)-(1/18)*sqrt(3)/n+(1/648)*sqrt(3)/n^2 +(463/174960)*sqrt(3)/n^3+O(1/n^4))*(3^n)^3/(((1/n)^n)^2*(exp(n))^2*2^n), n->infinity.
%F A166334 E.g.f.: (of aerated sequence) 2*sqrt(2)*cos(arcsin((3*sqrt(6)x/4)/3))/sqrt(8-27x^2). - _Paul Barry_, Jul 27 2010
%F A166334 2*a(n) = 3*(3*n-1)*(3*n-2)*a(n-1). - _R. J. Mathar_, Jul 24 2012
%t A166334 Table[(3*n)!/(2^n*n!), {n, 0, 10}] (* _G. C. Greubel_, May 09 2016 *)
%o A166334 (Magma) [Factorial(3*n)/(2^n*Factorial(n)): n in [0..20]]; // _Vincenzo Librandi_, May 10 2016
%K A166334 nonn
%O A166334 0,2
%A A166334 _Karol A. Penson_, Oct 12 2009