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 A384470 #8 May 30 2025 10:06:25
%S A384470 1,2,29,1108,82924,10302768,1917699552,499332175200,173242955039616,
%T A384470 77238974345915520,43027312823342164800,29285800226400628915200,
%U A384470 23913110797474508388449280,23071378298963178620672409600,25964692904608781751347296204800,33711625062334209438536728660070400
%N A384470 a(n) = n! * Sum_{k=0..n} Stirling2(2*k,k) * Stirling2(2*n-2*k,n-k) / binomial(n,k).
%F A384470 a(n) ~ 2^(2*n+1) * n^(2*n) / (sqrt(1-w) * exp(2*n) * (2-w)^n * w^n), where w = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599...
%t A384470 Table[n! * Sum[StirlingS2[2*k, k] * StirlingS2[2*n-2*k, n-k] / Binomial[n, k], {k, 0, n}], {n, 0, 20}]
%Y A384470 Cf. A187655, A187657, A384471, A384472.
%Y A384470 Cf. A226775.
%K A384470 nonn
%O A384470 0,2
%A A384470 _Vaclav Kotesovec_, May 30 2025