A376493 E.g.f. satisfies A(x) = exp(x^3 * (1 + x) * A(x)^3).

1, 0, 0, 6, 24, 0, 2520, 35280, 141120, 6048000, 181440000, 1995840000, 51831964800, 2280127449600, 47882676441600, 1192991325926400, 59048471978496000, 1942527607308288000, 56983429057076121600, 2842216483159788134400, 126830901998902413312000

Offset: 0

Author

Seiichi Manyama, Sep 25 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A362771, A376492.

Cf. A376477.

Programs

PARI

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

PARI

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

Formula

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

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