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
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
-
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!);
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!.