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 A296591 #13 Feb 16 2025 08:33:52
%S A296591 1,2,288,12441600,421382062080000,23120161750363668480000000,
%T A296591 3683853104727992382799761899520000000000,
%U A296591 2777528195026874073410445622205453260145295360000000000000
%N A296591 a(n) = Product_{k=0..n} (n + k)!.
%H A296591 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>.
%H A296591 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>
%F A296591 a(n) = BarnesG(2*n + 2) / BarnesG(n + 1).
%F A296591 a(n) ~ 2^(2*n^2 + 5*n/2 + 11/12) * n^((n+1)*(3*n+1)/2) * Pi^((n+1)/2) / exp(9*n^2/4 + 2*n).
%p A296591 a:= proc(n) option remember; `if`(n=0, 1,
%p A296591 a(n-1) *(2*n-1)! *(2*n)! /(n-1)!)
%p A296591 end:
%p A296591 seq(a(n), n=0..7); # _Alois P. Heinz_, Jul 11 2024
%t A296591 Table[Product[(n + k)!, {k, 0, n}], {n, 0, 10}]
%t A296591 Table[Product[(2*n - k)!, {k, 0, n}], {n, 0, 10}]
%t A296591 Table[BarnesG[2*n + 2]/BarnesG[n + 1], {n, 0, 10}]
%Y A296591 Cf. A001142, A007685, A086205, A098694, A110131, A112332, A268196, A296589, A296590.
%K A296591 nonn
%O A296591 0,2
%A A296591 _Vaclav Kotesovec_, Dec 16 2017
%E A296591 Missing a(0)=1 inserted by _Georg Fischer_, Nov 18 2021