A377530 Expansion of e.g.f. 1/(1 - x * exp(x))^3.
1, 3, 18, 141, 1380, 16095, 217458, 3335745, 57225528, 1085066523, 22526087070, 508042140573, 12367076890644, 323130848000727, 9018976230237834, 267789942962863065, 8427492557547704688, 280194087519310655667, 9813332205452943323190, 361109786425470021564021
Offset: 0
Programs
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Mathematica
nmax=19; CoefficientList[Series[1/(1 - x * Exp[x])^3,{x,0,nmax}],x]Range[0,nmax]! (* Stefano Spezia, Feb 05 2025 *) -
PARI
a(n) = n!*sum(k=0, n, k^(n-k)*binomial(k+2, 2)/(n-k)!);
Formula
a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(k+2,2)/(n-k)!.
a(n) ~ n! * n^2 / (2 * (1+LambertW(1))^3 * LambertW(1)^n). - Vaclav Kotesovec, Oct 31 2024