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 A384491 #11 May 31 2025 09:34:35
%S A384491 1,2,57,6536,1966816,1226860992,1373652478656,2507498281198080,
%T A384491 6966291361870181376,27969794062091821670400,
%U A384491 155875927262331497576140800,1167389777699203314381963264000,11441270265465265986005655905894400,143525982910350708912088976768630784000
%N A384491 a(n) = n!^2 * Sum_{k=0..n} Stirling2(2*k,k) * Stirling2(2*n-2*k,n-k) / binomial(n,k)^2.
%F A384491 a(n) ~ sqrt(Pi) * 2^(2*n + 3/2) * n^(3*n + 1/2) / (sqrt(1-w) * exp(3*n) * (2-w)^n * w^n), where w = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599...
%t A384491 Table[n!^2 * Sum[StirlingS2[2*k, k] * StirlingS2[2*n-2*k, n-k] / Binomial[n, k]^2, {k, 0, n}], {n, 0, 15}]
%o A384491 (PARI) a(n) = n!^2 * sum(k=0, n, stirling(2*k,k, 2) * stirling(2*n-2*k,n-k,2) / binomial(n,k)^2); \\ _Michel Marcus_, May 31 2025
%Y A384491 Cf. A187655, A384470, A384492.
%Y A384491 Cf. A187657, A384471, A384472.
%K A384491 nonn
%O A384491 0,2
%A A384491 _Vaclav Kotesovec_, May 31 2025