A377608 - OEIS

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

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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!);