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 A368686 #4 Jan 03 2024 03:40:35
%S A368686 0,12,172800,1536288768000,16189465114548633600000,
%T A368686 322110526445545505917029580800000000,
%U A368686 17555281051920416386104936570114748195012608000000000,3580285185706909590176164870311607533516764550107699116769280000000000000
%N A368686 a(n) = Product_{j=0..n, k=0..n} (j + k + n).
%F A368686 For n>0, a(n) = 3*n*BarnesG(n) * BarnesG(3*n) * Gamma(3*n)^2 / BarnesG(2*n+1)^2.
%F A368686 a(n) ~ 3^(9*n^2/2 + 3*n + 5/12) * n^((n+1)^2) / (2^(4*n^2 - 1/6) * exp(3*n^2/2 + 2*n)).
%F A368686 a(n) = 4*n*Gamma(2*n)^2 * A368685(n) / Gamma(n)^2.
%t A368686 Table[Product[i+j+n, {i, 0, n}, {j, 0, n}], {n, 0, 8}]
%t A368686 Join[{0}, Table[3*n*BarnesG[n] * BarnesG[3*n] * Gamma[3*n]^2 / BarnesG[2*n+1]^2, {n, 1, 8}]]
%Y A368686 Cf. A079478, A306594, A324444, A368622, A368685.
%K A368686 nonn
%O A368686 0,2
%A A368686 _Vaclav Kotesovec_, Jan 03 2024