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

0,3

Links

Table of n, a(n) for n=0..19.

Eric Weisstein's World of Mathematics, Lambert W-Function.

Wikipedia, Lambert W function.

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

Prog

(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-x*exp(x^2)))))

Crossrefs

Cf. A216857, A360433.

Cf. A052318.

Sequence in context: A022026 A026113 A052874 * A376327 A074622 A031507

Adjacent sequences: A360429 A360430 A360431 * A360433 A360434 A360435

Keyword

nonn

Author

Seiichi Manyama, Feb 07 2023

Status

approved