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%I #12 Aug 18 2023 08:26:30
%S 1,1,3,-5,-23,521,-1829,-71021,1319697,5905297,-683965709,8664974891,
%T 311864420473,-13981842414695,6694007756619,16448800124183491,
%U -448649039951220959,-13236887251789967071,1210629233913421852387,-12065049302884271631269
%N E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^2)).
%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(2*x^2*exp(-2*x))/2 ).
%F a(n) = n! * Sum_{k=0..n} (-2*n+2*k+1)^(k-1) * binomial(k,n-k)/k!.
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(2*x^2*exp(-2*x))/2)))
%Y Cf. A125500, A143768, A363354, A363529, A365035, A365037.
%Y Cf. A361091.
%K sign
%O 0,3
%A _Seiichi Manyama_, Aug 17 2023