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%I #8 Mar 03 2019 05:55:09
%S 0,1,288,125411328000,6658606584104736522240000000,
%T 792786697595796795607377086400871488552960000000000000
%N a(n) = BarnesG(3*n).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>
%F a(n) = A^8 * exp(-2/3) * 3^(9*n^2/2 - 3*n + 5/12) * (2*Pi)^(1 - 3*n) * BarnesG(n) * BarnesG(n + 1/3)^2 * BarnesG(n + 2/3)^3 * BarnesG(n+1)^2 * BarnesG(n + 4/3), where A is the Glaisher-Kinkelin constant A074962.
%F a(n) ~ 3^(9*n^2/2 - 3*n + 5/12) * n^(9*n^2/2 - 3*n + 5/12) * (2*Pi)^((3*n-1)/2) / (A * exp(27*n^2/4 - 3*n - 1/12)), where A is the Glaisher-Kinkelin constant A074962.
%t Table[BarnesG[3*n], {n, 0, 10}]
%t Round[Table[Glaisher^8 * E^(-2/3) * 3^(9*n^2/2 - 3*n + 5/12) * (2*Pi)^(1 - 3*n) * BarnesG[n] * BarnesG[n + 1/3]^2 * BarnesG[n + 2/3]^3 * BarnesG[n + 1]^2 * BarnesG[n + 4/3], {n, 0, 10}]]
%Y Cf. A000178, A268504, A296607, A306651.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Dec 16 2017
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