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 A296589 #10 Feb 16 2025 08:33:52
%S A296589 1,2,24,1800,878080,2857680000,63117561830400,9577928124440387712,
%T A296589 10077943267571584204800000,74054886893191804566576837427200,
%U A296589 3822038592032831128918160803430400000000,1391938996758770867922655936144556115037409280000
%N A296589 a(n) = Product_{k=0..n} binomial(2*n, k).
%H A296589 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>.
%H A296589 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>
%F A296589 a(n) = ((2*n)!)^(n+1) / (n! * BarnesG(2*n + 2)).
%F A296589 a(n) ~ A * exp(n^2 + n - 1/24) / (2^(5/12) * Pi^((n+1)/2) * n^(n/2 + 5/12)), where A is the Glaisher-Kinkelin constant A074962.
%t A296589 Table[Product[Binomial[2*n, k], {k, 0, n}], {n, 0, 12}]
%t A296589 Table[((2*n)!)^(n+1) / (n! * BarnesG[2*n + 2]), {n, 0, 12}]
%Y A296589 Cf. A001142, A007685, A086205, A110131, A112332, A268196, A296590, A296591.
%K A296589 nonn
%O A296589 0,2
%A A296589 _Vaclav Kotesovec_, Dec 16 2017
%E A296589 Missing a(0)=1 inserted by _Georg Fischer_, Nov 18 2021