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%I #14 Apr 16 2023 15:55:16
%S 1,1,1,-5,-31,-99,1201,13231,70785,-1362311,-21562399,-161746749,
%T 4263108961,87979472725,849097038609,-28416142768649,-723086288422399,
%U -8532476619366159,346207723221680065,10474480743776327179,146105160034616914401
%N a(n) = n! * Sum_{k=0..floor(n/3)} (-n/3)^k * binomial(n-2*k,k)/(n-2*k)!.
%H Winston de Greef, <a href="/A362304/b362304.txt">Table of n, a(n) for n = 0..425</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F a(n) = A362302(n,2*n).
%F a(n) = n! * [x^n] exp(x - n*x^3/3).
%F E.g.f.: exp( ( LambertW(x^3) )^(1/3) ) / (1 + LambertW(x^3)).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(x^3)^(1/3))/(1+lambertw(x^3))))
%Y Cf. A362300, A362302.
%K sign
%O 0,4
%A _Seiichi Manyama_, Apr 15 2023