A377595 E.g.f. satisfies A(x) = exp( x * A(x) / (1-x) ) / (1-x).

1, 2, 11, 103, 1377, 24101, 523813, 13636463, 414246017, 14396807161, 563682761541, 24559156435595, 1178780540094193, 61810491468265541, 3515914378433242997, 215647516162031069191, 14187967957218808201089, 996767406049512569338481, 74478502236949781909301253

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

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

a(n) ~ sqrt(1 + 2*exp(-1) - sqrt(1 + 4*exp(-1))) * sqrt(1 + 4*exp(-1) - sqrt(1 + 4*exp(-1))) * 2^(n + 3/2) * n^(n-1) / ((sqrt(1 + 4*exp(-1)) - 1)^(5/2) * exp(n) * (2 + exp(1) - exp(1/2)*sqrt(4 + exp(1)))^n). - Vaclav Kotesovec, Aug 05 2025

Prog

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

Crossrefs

Cf. A362775, A377810.

Cf. A361598.

Sequence in context: A081716 A385767 A334240 * A099713 A277461 A277470

Adjacent sequences: A377592 A377593 A377594 * A377596 A377597 A377598

Keyword

nonn

Author

Seiichi Manyama, Nov 14 2024

Status

approved