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%I #6 Jul 05 2021 09:09:39
%S 1,2,15,263,8450,432514,32308948,3317537208,448304831744,
%T 77131843774416,16463316260454624,4269057157148962320,
%U 1321883141629335120576,481761671427370573812000,204137795884403682574690176,99514256070766872294586292544
%N a(n) = sum(abs(stirling1(n+1,k+1))*stirling2(n+1,k+1)*k!^2,k=0..n).
%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 = 1.333855551736054319768931910172827342915539397625400733803588773... - _Vaclav Kotesovec_, Jul 05 2021
%t Table[Sum[Abs[StirlingS1[n+1,k+1]]StirlingS2[n+1,k+1]k!^2,{k,0,n}],{n,0,100}]
%o (Maxima) makelist(sum(abs(stirling1(n+1,k+1))*stirling2(n+1,k+1)*k!^2,k,0,n),n,0,24);
%K nonn
%O 0,2
%A _Emanuele Munarini_, Jul 04 2011
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