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%I #16 Apr 18 2023 08:28:09
%S 1,1,1,7,25,61,1561,10291,40657,1754425,16632721,90479071,5469933481,
%T 67591594357,468224398825,36386954606731,554182030325281,
%U 4663003095358321,442756825853252257,8014853488848923575,79354642490200806841,8901962495566386752941
%N a(n) = n! * Sum_{k=0..floor(n/3)} k^k / (k! * (n-3*k)!).
%H Seiichi Manyama, <a href="/A362348/b362348.txt">Table of n, a(n) for n = 0..427</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F E.g.f.: exp(x) / (1 + LambertW(-x^3)).
%F 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
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^3))))
%Y Cf. A086331, A362347, A362349.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Apr 17 2023
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