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A192565 a(n) = sum(abs(stirling1(n+1,k+1))*stirling2(n,k)*k!^2,k=0..n). 0

%I

%S 1,1,7,119,3766,191074,14190940,1451180016,195500153984,

%T 33556323694176,7148802130010784,1850863101948856368,

%U 572367322411341168960,208372437783910651168800,88211625475147231105812096,42967145403522500557662391104

%N a(n) = sum(abs(stirling1(n+1,k+1))*stirling2(n,k)*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 = 0.5694875599509546909505843910919946016728003129830561427442509356... - _Vaclav Kotesovec_, Jul 05 2021

%t Table[Sum[Abs[StirlingS1[n+1,k+1]]StirlingS2[n,k]k!^2,{k,0,n}],{n,0,100}]

%o (Maxima) makelist(sum(abs(stirling1(n+1,k+1))*stirling2(n,k)*k!^2,k,0,n),n,0,24);

%K nonn

%O 0,3

%A _Emanuele Munarini_, Jul 04 2011

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Last modified May 22 13:12 EDT 2022. Contains 353950 sequences. (Running on oeis4.)