A361194 E.g.f. satisfies A(x) = exp( -3*x*A(x) ) / (1-x).

1, -2, 17, -237, 4893, -133683, 4567905, -187666587, 9017657433, -496470972951, 30824023641669, -2131090659947439, 162397790115179733, -13525005928296072915, 1222285110682680848169, -119135392516302191619507, 12458374493322416970025521

Offset: 0

Author

Seiichi Manyama, Mar 03 2023

Keywords

• sign

Links

• Winston de Greef, Table of n, a(n) for n = 0..338
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A352410, A352448, A361182, A361193.

Cf. A361069.

Programs

PARI

a(n) = n!*sum(k=0, n, (-3)^k*(k+1)^(k-1)*binomial(n, k)/k!);

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(lambertw(3*x/(1-x))/(3*x)))

Formula

a(n) = n! * Sum_{k=0..n} (-3)^k * (k+1)^(k-1) * binomial(n,k)/k!.

E.g.f.: LambertW( 3*x/(1-x) ) / (3*x).