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 A372140 #8 Feb 16 2025 08:34:06
%S A372140 1,1,1,1,16,3981312,2271857773302207479808,
%T A372140 133781874275586180035265927852035878702421114880000000
%N A372140 a(n) = Product_{k=1..n} BarnesG(k)^k.
%C A372140 The next term has 113 digits.
%H A372140 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>.
%H A372140 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>.
%F A372140 a(n) ~ (2*Pi)^(n*(n^2 - 1)/6) * n^(n^4/8 - n^3/12 - n^2/6 + n/24 + 19/720) / (A^(n^2/2 + n/2 - 1/3) * exp(7*n^4/32 - 5*n^3/72 - 7*n^2/24 - n/24 - zeta(3)/(8*Pi^2) + zeta'(-3)/6 + 23/720)), where A is the Glaisher-Kinkelin constant A074962, zeta(3) = A002117, zeta'(-3) = A259068.
%t A372140 Table[Product[BarnesG[k]^k, {k, 1, n}], {n, 0, 8}]
%Y A372140 Cf. A055462, A255269.
%K A372140 nonn
%O A372140 0,5
%A A372140 _Vaclav Kotesovec_, Apr 20 2024