A360484 E.g.f. satisfies A(x) = x * exp(x - 3 * A(x)).

0, 1, -4, 48, -896, 22880, -743232, 29337280, -1363752448, 72979407360, -4419108684800, 298730433250304, -22300928914403328, 1822195561572585472, -161756111552270491648, 15501595224386724126720, -1595092357302221461127168, 175405731698165304882495488

Offset: 0

Author

Seiichi Manyama, Feb 09 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A216857, A360481, A360482, A360483.

Programs

PARI

my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(lambertw(3*x*exp(x))/3)))

PARI

a(n) = sum(k=1, n, (-3)^(k-1)*k^(n-1)*binomial(n, k));

Formula

E.g.f.: A(x) = LambertW(3*x * exp(x))/3.

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