A377529 Expansion of e.g.f. 1/(1 - x * exp(x))^2.
1, 2, 10, 66, 560, 5770, 69852, 970886, 15228880, 266006610, 5119447700, 107617719022, 2453167135608, 60268223308826, 1587381621990556, 44619277892537910, 1333135910963656352, 42189279001183102882, 1409741875877923927332, 49597905017847180008126
Offset: 0
Programs
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Mathematica
With[{nn=20},CoefficientList[Series[1/(1-x Exp[x])^2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Feb 04 2025 *) -
PARI
a(n) = n!*sum(k=0, n, (k+1)*k^(n-k)/(n-k)!);
Formula
a(n) = n! * Sum_{k=0..n} (k+1) * k^(n-k)/(n-k)!.
a(n) ~ n! * n/((1 + LambertW(1))^2 * LambertW(1)^n). - Vaclav Kotesovec, Oct 31 2024