A358081 Expansion of e.g.f. 1/(1 - x^3 * exp(x)).

1, 0, 0, 6, 24, 60, 840, 10290, 80976, 847224, 13306320, 190271070, 2677088040, 46082426676, 874515884424, 16582066303530, 336875275380000, 7539189088358640, 176554878235711776, 4295134487197296054, 111114287924643309240, 3036073975138066955820

Offset: 0

Author

Seiichi Manyama, Oct 30 2022

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..431

Crossrefs

Cf. A006153, A358080.

Cf. A292889, A355575, A358065.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[1/(1-x^3 Exp[x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Aug 12 2025 *)

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^3*exp(x))))

PARI

a(n) = n!*sum(k=0, n\3, k^(n-3*k)/(n-3*k)!);

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} k^(n - 3*k)/(n - 3*k)!.

a(n) ~ n! / ((1 + LambertW(1/3)) * 3^(n+1) * LambertW(1/3)^n). - Vaclav Kotesovec, Oct 30 2022