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A192564 a(n) = sum(abs(stirling1(n,k))*stirling2(n,k)*k!^2,k=0..n). 0

%I #10 Jul 05 2021 09:07:39

%S 1,1,5,74,2186,106524,7703896,773034912,102673179360,17429291711280,

%T 3680338415133024,945958227345434016,290761516548473591232,

%U 105309706114422166775040,44384982810939832477305600,21536846291826596564956445184

%N a(n) = sum(abs(stirling1(n,k))*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 = 0.27034346270211507329954765593360596752557904498770241464597402478625037569... - _Vaclav Kotesovec_, Jul 05 2021

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

%o (Maxima) makelist(sum(abs(stirling1(n,k))*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 March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)