A361193 E.g.f. satisfies A(x) = exp( -2*x*A(x) ) / (1-x).

1, -1, 6, -50, 648, -10952, 232336, -5919664, 176435328, -6024464000, 231972167424, -9946181374208, 470038191434752, -24276240445152256, 1360508977539004416, -82233680186863536128, 5332689963474238341120, -369321737420738845638656

Offset: 0

Author

Seiichi Manyama, Mar 03 2023

Keywords

• sign

Links

• Winston de Greef, Table of n, a(n) for n = 0..360
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A352410, A352448, A361182, A361194.

Cf. A361068.

Programs

PARI

a(n) = n!*sum(k=0, n, (-2)^k*(k+1)^(k-1)*binomial(n, k)/k!);

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(lambertw(2*x/(1-x))/(2*x)))

Formula

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

E.g.f.: LambertW( 2*x/(1-x) ) / (2*x).