%I #10 Dec 17 2023 08:06:36
%S 0,0,1,2,3,6,29,604,69724,49836144,250872492816,10113420362487552,
%T 3669877057922582621184,13317216838086531218401935360,
%U 531580547910000731718546175028428800,254627927130379381409123944181515703549952000
%N a(n) = Sum_{k=0..n} BarnesG(k)*BarnesG(n-k).
%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) ~ 2^(n/2) * Pi^(n/2 - 1) * n^(n^2/2 - 2*n + 23/12) / (A * exp(3*n^2/4 - 2*n - 1/12)), where A = A074962 is the Glaisher-Kinkelin constant.
%t Table[Sum[BarnesG[k]*BarnesG[n-k], {k, 0, n}], {n, 0, 15}]
%Y Cf. A000178, A003149.
%K nonn
%O 0,4
%A _Vaclav Kotesovec_, Dec 17 2023