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%I #8 Dec 26 2023 09:56:21
%S 1,1,7,122,3926,201444,15081256,1551423600,209964727584,
%T 36170279518320,7728442094221344,2005825817037374496,
%U 621563279659462241856,226678766174046141016320,96106307573596013377908480,46874174201481263768233403904
%N a(n) = Sum_{k=0..n} abs(stirling1(n,k))*stirling2(n+1,k+1)*k!^2.
%F 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 = 0.63319930751748217157127596837987799731063242340102342707708047131... - _Vaclav Kotesovec_, Jul 05 2021
%t Table[Sum[Abs[StirlingS1[n,k]]StirlingS2[n+1,k+1]k!^2,{k,0,n}],{n,0,100}]
%o (Maxima) makelist(sum(abs(stirling1(n,k))*stirling2(n+1,k+1)*k!^2,k,0,n),n,0,24);
%K nonn
%O 0,3
%A _Emanuele Munarini_, Jul 04 2011
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