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A362348
a(n) = n! * Sum_{k=0..floor(n/3)} k^k / (k! * (n-3*k)!).
7
1, 1, 1, 7, 25, 61, 1561, 10291, 40657, 1754425, 16632721, 90479071, 5469933481, 67591594357, 468224398825, 36386954606731, 554182030325281, 4663003095358321, 442756825853252257, 8014853488848923575, 79354642490200806841, 8901962495566386752941
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp(x) / (1 + LambertW(-x^3)).
a(n) ~ (exp(3*exp(-1/3)/2) + 2*cos(sqrt(3)*exp(-1/3)/2 - 2*Pi*n/3)) * n^n / (sqrt(3) * exp(2*n/3 + exp(-1/3)/2)). - Vaclav Kotesovec, Apr 18 2023
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^3))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 17 2023
STATUS
approved