A376495 E.g.f. satisfies A(x) = exp(x^3 * A(x)^3 / (1 - x)).

1, 0, 0, 6, 24, 120, 3240, 40320, 463680, 11491200, 248572800, 4869849600, 135896745600, 4017466252800, 113150157120000, 3765622699238400, 137549036072448000, 5019223860338688000, 199794776937044889600, 8636618647667288678400

Offset: 0

Author

Seiichi Manyama, Sep 25 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A052868, A376494.

Cf. A376475.

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(n-2*k-1, 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(n-2*k-1,n-3*k)/k!.