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%I #14 Feb 07 2023 12:42:46
%S 0,1,2,15,112,1225,16896,283759,5623808,128431377,3321026560,
%T 95915951791,3060250165248,106896447626137,4057412577591296,
%U 166284754020913935,7318183421113532416,344228133020323687201,17233838271273426223104,915000759922243030582735
%N E.g.f. satisfies A(x) = x * exp(A(x) + x^2).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lambert_W_function">Lambert W function</a>.
%F E.g.f.: -LambertW( -x*exp(x^2) ).
%F a(n) ~ sqrt(1+LambertW(2*exp(-2))) * 2^(n/2) * n^(n-1) / (exp(n) * (LambertW(2*exp(-2)))^(n/2)). - _Vaclav Kotesovec_, Feb 07 2023
%o (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-x*exp(x^2)))))
%Y Cf. A216857, A360433.
%Y Cf. A052318.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Feb 07 2023