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 A306635 #23 Jul 24 2025 13:33:58
%S A306635 1,2,576,14332723200,72474629486854275072000000,
%T A306635 482580045081719158086051946616717605601280000000000000
%N A306635 a(n) = Product_{k=1..n} BarnesG(2*k).
%C A306635 Next term is too long to be included.
%H A306635 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>.
%H A306635 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>
%F A306635 a(n) ~ c * 2^(2*n^3/3 + n^2/2 - n/4 - 3/8) * n^(2*n^3/3 - n/4) * Pi^(n^2/2 - 3/8) / (A^(n-2) * exp(11*n^3/9 - n/3 - Zeta(3)/(2*Pi^2) + 1/12)), where c = A255674^2 = 1.1446513373245340524595435844492841792576337833610236993... and A is the Glaisher-Kinkelin constant A074962.
%F A306635 a(n) ~ 2^(2*n^3/3 + n^2/2 - n/4 - 1/8) * n^(2*n^3/3 - n/4) * Pi^(n^2/2) / (A^n * exp(11*n^3/9 - n/3 - Zeta(3)/(16*Pi^2))), where A is the Glaisher-Kinkelin constant A074962.
%F A306635 a(n) = a(n-1)*A296607(n). - _R. J. Mathar_, Jul 24 2025
%t A306635 Table[Product[BarnesG[2*k], {k, 1, n}], {n, 1, 8}]
%t A306635 Round[Table[2^(2*n^3/3 + n^2 - 5*n/3 - 2/3) * E^(n^3/2 + 3*n^2/4 + n/4 + 1/12 - 3*Zeta[3]/(16*Pi^2) + 2*PolyGamma[-3, n + 1] + Derivative[1, 0][Zeta][-2, n + 1/2] + 2*Derivative[1, 0][Zeta][-1, n + 1/2]) * Gamma[n]^(2*n - 7/4) * BarnesG[2*n]^(n + 1) / (Glaisher^(2*n + 3) * Pi^(n^2/2 + n + 1/2) * n^(n^2) * Gamma[2*n]^(n^2 + n - 3/4) * BarnesG[n]^2), {n, 1, 8}]] (* _Vaclav Kotesovec_, Mar 04 2019 *)
%Y A306635 Cf. A055462, A168467, A255674, A296607, A306651, A324992.
%K A306635 nonn
%O A306635 1,2
%A A306635 _Vaclav Kotesovec_, Mar 02 2019