A357948 Expansion of e.g.f. exp( x * exp(-x^2) ).

1, 1, 1, -5, -23, 1, 601, 2731, -13775, -219743, -313199, 15383611, 125451481, -811558175, -20767068503, -37852036949, 2898343066081, 28990920216001, -313289894357855, -8634009894555653, -3214642669500599, 2108734127922999361, 20183394611962437241

Offset: 0

Author

Seiichi Manyama, Oct 29 2022

Keywords

• sign
• easy

Crossrefs

Cf. A003725, A358063.

Cf. A216688.

Programs

PARI

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

PARI

a(n) = n!*sum(k=0, n\2, (-n+2*k)^k/(k!*(n-2*k)!));

Formula

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