A362396 E.g.f. satisfies A(x) = exp(x - x^2 * A(x)).

1, 1, -1, -11, -11, 381, 2461, -21083, -449623, 221113, 99327961, 862237641, -24117649907, -612442461227, 3958786971413, 388794711373741, 2915530533136081, -239559177608638095, -6208842113295032015, 118603625804273873809, 8571701737898867135861

Offset: 0

Author

Seiichi Manyama, Apr 20 2023

Keywords

• sign

Links

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

Crossrefs

Column k=2 of A362394.

Cf. A362430, A362431.

Cf. A125500.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^2*exp(x)))))

Formula

E.g.f.: exp(x - LambertW(x^2 * exp(x))) = LambertW(x^2 * exp(x))/x^2.

a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * (k+1)^(n-k-1) / (k! * (n-2*k)!).