A377811 E.g.f. satisfies A(x) = exp(x * A(x)) / (1 - x)^3.

1, 4, 27, 283, 4217, 82971, 2041855, 60475885, 2096566449, 83324680435, 3736041351311, 186594364199277, 10274269171279657, 618386703880855339, 40393224245061185919, 2846030947359659421901, 215160957844217080056161, 17373449685399138641312739, 1492298627191467511376377999

Offset: 0

Author

Seiichi Manyama, Nov 08 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A352410, A377810.

Cf. A082030, A367789, A377743.

Programs

PARI

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

PARI

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

Formula

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

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

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