A377608 - OEIS

%I #38 Feb 16 2025 08:34:07

%S 1,3,19,202,3085,61886,1544029,46182900,1612759369,64455582394,

%T 2902794546961,145497909334856,8035136800888333,484821204654219798,

%U 31735810390729211173,2240132583683741633116,169624462686462529305745,13715713402047448280358002,1179576532854283015832748697

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

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

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

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

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^3))/(1-x)^2))

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

%Y Cf. A367789, A377599, A377811.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 14 2024