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 A192564 #15 Apr 08 2025 11:30:04
%S A192564 1,1,5,74,2186,106524,7703896,773034912,102673179360,17429291711280,
%T A192564 3680338415133024,945958227345434016,290761516548473591232,
%U A192564 105309706114422166775040,44384982810939832477305600,21536846291826596564956445184
%N A192564 a(n) = Sum_{k=0..n} abs(Stirling1(n,k))*Stirling2(n,k)*(k!)^2.
%F A192564 a(n) ~ c * LambertW(-1, -r*exp(-r))^n * n!^2 / (sqrt(n) * LambertW(-exp(-1/r)/r)^n), where r = 0.673313285145753168... is the root of the equation (1 + 1/(r*LambertW(-exp(-1/r)/r))) * (r + LambertW(-1, -r*exp(-r))) = 1 and c = 0.27034346270211507329954765593360596752557904498770241464597402478625037569... - _Vaclav Kotesovec_, Jul 05 2021
%F A192564 a(n) = (n!)^2 * [(x*y)^n] 1 / (1 + (exp(x) - 1) * log(1 - y)). - _Ilya Gutkovskiy_, Apr 06 2025
%t A192564 Table[Sum[Abs[StirlingS1[n,k]]StirlingS2[n,k]k!^2,{k,0,n}],{n,0,100}]
%t A192564 nmax = 20; Table[SeriesCoefficient[1/(1 + (E^x - 1)*Log[1 - y]), {x, 0, n}, {y, 0, n}], {n, 0, nmax}] * Range[0, nmax]!^2 (* _Vaclav Kotesovec_, Apr 08 2025 *)
%o A192564 (Maxima) makelist(sum(abs(stirling1(n,k))*stirling2(n,k)*k!^2,k,0,n),n,0,24);
%Y A192564 Cf. A047793, A048144, A382792.
%K A192564 nonn
%O A192564 0,3
%A A192564 _Emanuele Munarini_, Jul 04 2011