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%I #10 Aug 18 2023 08:26:34
%S 1,1,3,-11,-11,1341,-14339,-168923,8905065,-85313735,-4604578919,
%T 197455645641,-273728455571,-267002430142187,9427821270512373,
%U 178475402982086701,-28273343910563670959,713736314833387866225,51907546734507018043057
%N E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^3)).
%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^2*exp(-3*x))/3 ).
%F a(n) = n! * Sum_{k=0..n} (-3*n+3*k+1)^(k-1) * binomial(k,n-k)/k!.
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(3*x^2*exp(-3*x))/3)))
%Y Cf. A125500, A143768, A363354, A363529, A365035, A365036.
%Y Cf. A361092.
%K sign
%O 0,3
%A _Seiichi Manyama_, Aug 17 2023