A377608 E.g.f. satisfies A(x) = exp( x * A(x) / (1-x) ) / (1-x)^2.

1, 3, 19, 202, 3085, 61886, 1544029, 46182900, 1612759369, 64455582394, 2902794546961, 145497909334856, 8035136800888333, 484821204654219798, 31735810390729211173, 2240132583683741633116, 169624462686462529305745, 13715713402047448280358002, 1179576532854283015832748697

Offset

0,2

Links

Table of n, a(n) for n=0..18.

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

Formula

E.g.f.: exp( -LambertW(-x/(1-x)^3) )/(1-x)^2.

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^3))/(1-x)^2))
(PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+2*k+1, n-k)/k!);

Crossrefs

Cf. A367789, A377599, A377811.

Sequence in context: A208897 A027546 A301419 * A201827 A230321 A108993

Adjacent sequences: A377605 A377606 A377607 * A377609 A377610 A377611

Keyword

nonn

Author

Seiichi Manyama, Nov 14 2024

Status

approved