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%I #21 Apr 23 2023 02:06:35
%S 1,1,1,7,97,961,10201,177241,3801505,80718625,1887205681,52896262321,
%T 1648697978401,54216677033377,1928791931034697,75326014326206281,
%U 3159713152034201281,140373558362282197441,6632746205445950124385,333591744669464008432225
%N E.g.f. satisfies A(x) = exp(x + x^3 * A(x)^3).
%H Seiichi Manyama, <a href="/A362472/b362472.txt">Table of n, a(n) for n = 0..384</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 - LambertW(-3*x^3 * exp(3*x))/3) = ( -LambertW(-3*x^3 * exp(3*x))/(3*x^3) )^(1/3).
%F a(n) = n! * Sum_{k=0..floor(n/3)} (3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x^3*exp(3*x))/3)))
%Y Column k=6 of A362490.
%Y Cf. A143768, A349562, A362473.
%Y Cf. A362392, A362481.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Apr 21 2023
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