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 A268196 #20 Feb 16 2025 08:33:30
%S A268196 1,3,45,3780,1871100,5618913300,104309506501200,12129109415959536000,
%T A268196 8920608231265175901456000,41809329673499408044341517200000,
%U A268196 1256161937180234817183361549396758000000,243113461110708695347467432844366521953760000000
%N A268196 a(n) = Product_{k=0..n} binomial(3*k,k).
%H A268196 Harvey P. Dale, <a href="/A268196/b268196.txt">Table of n, a(n) for n = 0..49</a>
%H A268196 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>.
%H A268196 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>.
%F A268196 a(n) = A^(7/6) * Gamma(1/3)^(1/3) * 3^(3*n^2/2 + 2*n + 11/36)* BarnesG(n + 4/3) * BarnesG(n + 5/3) / (exp(7/72) * 2^(n^2 + 2*n + 5/8) * Pi^(n/2 + 5/12) * BarnesG(n + 3/2) * BarnesG(n + 2)), where A = A074962 is the Glaisher-Kinkelin constant.
%F A268196 a(n) ~ A^(7/6) * Gamma(1/3)^(1/3) * 3^(11/36 + 2*n + 3*n^2/2) * exp(n/2 - 7/72) / (2^(n^2 + 2*n + 7/8) * Pi^(n/2 + 2/3) * n^(n/2 + 25/72)), where A = A074962 is the Glaisher-Kinkelin constant.
%F A268196 a(n) = A268504(n) / (A000178(n) * A098694(n)).
%t A268196 Table[Product[Binomial[3k,k],{k,0,n}],{n,0,12}]
%t A268196 FoldList[Times,Table[Binomial[3n,n],{n,0,15}]] (* _Harvey P. Dale_, Apr 23 2018 *)
%Y A268196 Cf. A001142, A005809, A007685, A086205, A112332, A268504, A262261.
%K A268196 nonn,easy
%O A268196 0,2
%A A268196 _Vaclav Kotesovec_, Apr 16 2016