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 A384471 #7 May 30 2025 10:06:29
%S A384471 1,2,18,306,8046,296100,14307254,865996306,63308257198,5432272670376,
%T A384471 535074966419260,59461066810476232,7354069129792197762,
%U A384471 1001371912804041913056,148806933109572134044158,23958722845801073318076450,4154065510530807075869275150,771608888261061026185781127184
%N A384471 a(n) = Sum_{k=0..n} binomial(n,k)^2 * Stirling2(2*k,k) * Stirling2(2*n-2*k,n-k).
%F A384471 a(n) ~ 2^(3*n + 1/2) * n^(n - 3/2) / (Pi^(3/2) * (1-w) * exp(n) * (2-w)^n * w^n), where w = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599...
%t A384471 Table[Sum[StirlingS2[2*k, k]*StirlingS2[2*n-2*k, n-k]*Binomial[n, k]^2, {k, 0, n}], {n, 0, 20}]
%Y A384471 Cf. A187655, A187657, A384470, A384472.
%Y A384471 Cf. A226775.
%K A384471 nonn
%O A384471 0,2
%A A384471 _Vaclav Kotesovec_, May 30 2025