A377595 - OEIS

%I #72 Feb 16 2025 08:34:07

%S 1,2,11,103,1377,24101,523813,13636463,414246017,14396807161,

%T 563682761541,24559156435595,1178780540094193,61810491468265541,

%U 3515914378433242997,215647516162031069191,14187967957218808201089,996767406049512569338481,74478502236949781909301253

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

%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)^2) )/(1-x).

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

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

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

%Y Cf. A362775, A377810.

%Y Cf. A361598.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 14 2024