A360432 E.g.f. satisfies A(x) = x * exp(A(x) + x^2).
0, 1, 2, 15, 112, 1225, 16896, 283759, 5623808, 128431377, 3321026560, 95915951791, 3060250165248, 106896447626137, 4057412577591296, 166284754020913935, 7318183421113532416, 344228133020323687201, 17233838271273426223104, 915000759922243030582735
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
- Wikipedia, Lambert W function.
Programs
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PARI
my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-x*exp(x^2)))))
Formula
E.g.f.: -LambertW( -x*exp(x^2) ).
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