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 A384028 #12 May 17 2025 13:58:32
%S A384028 1,13,2273,1184153,1251320145,2232012515445,6032418472347265,
%T A384028 23007314730623658225,117745011140615270168865,
%U A384028 778780810721500176081199325,6466413475830749109197652489569,65861328745485785925705177696147337,807448787241269228642562251336079833585
%N A384028 a(n) = Sum_{k=0..2*n} Stirling1(2*n+1, 2*n+1-k) * Stirling1(2*n+1, k+1).
%F A384028 a(n) ~ 2^(6*n) * w^(4*n + 3/2) * n^(2*n - 1/2) / (sqrt(Pi*(w-1)) * exp(2*n) * (2*w-1)^(2*n)), where w = -LambertW(-1, -exp(-1/2)/2) = 1.756431208626169676982737616...
%F A384028 a(n) = A129256(2*n) = [x^(2*n)] Product_{k=0..2*n} (1 + k*x)^2. - _Seiichi Manyama_, May 17 2025
%t A384028 Table[Sum[StirlingS1[2*n+1, 2*n+1-j]*StirlingS1[2*n+1, j+1], {j, 0, 2*n}], {n, 0, 15}]
%Y A384028 Cf. A129256, A234324.
%K A384028 nonn
%O A384028 0,2
%A A384028 _Vaclav Kotesovec_, May 17 2025