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%I #12 Aug 18 2023 08:26:38
%S 1,1,3,1,-11,61,301,-6299,7561,903673,-9019079,-145636919,4305630781,
%T 7516191541,-2037845181371,22442805921901,944219385367441,
%U -29922880660473359,-288352494154313999,32071808922904896913,-273044292430852251899
%N E.g.f. satisfies A(x) = exp(x * (1 + x/A(x))).
%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(x^2*exp(-x)) ).
%F a(n) = n! * Sum_{k=1..n} (-n+k+1)^(k-1) * binomial(k,n-k)/k! for n>0.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(x^2*exp(-x)))))
%Y Cf. A125500, A143768, A363354, A363529, A365036, A365037.
%Y Cf. A361090.
%K sign
%O 0,3
%A _Seiichi Manyama_, Aug 17 2023