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

0,2

Links

Table of n, a(n) for n=0..19.

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

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 *)

Prog

(PARI) a(n) = n!*sum(k=0, n, (k+1)*k^(n-k)/(n-k)!);

Crossrefs

Cf. A006153, A377530.

Cf. A377503, A377527.

Sequence in context: A361448 A376226 A346417 * A108205 A228938 A245000

Adjacent sequences: A377526 A377527 A377528 * A377530 A377531 A377532

Keyword

nonn,easy

Author

Seiichi Manyama, Oct 30 2024

Status

approved