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A358081
Expansion of e.g.f. 1/(1 - x^3 * exp(x)).
5
1, 0, 0, 6, 24, 60, 840, 10290, 80976, 847224, 13306320, 190271070, 2677088040, 46082426676, 874515884424, 16582066303530, 336875275380000, 7539189088358640, 176554878235711776, 4295134487197296054, 111114287924643309240, 3036073975138066955820
OFFSET
0,4
LINKS
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
PROG
(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)!);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Oct 30 2022
STATUS
approved