A102743 Expansion of e.g.f. LambertW(-x)/(x*(x-1)).

1, 2, 7, 37, 273, 2661, 32773, 491555, 8715409, 178438681, 4142334501, 107483043735, 3081956918857, 96759352320437, 3300826000845493, 121569984050610331, 4807542796319581089, 203167758634027130289

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

a(n) = n!*Sum_{k=1..n+1} k^(k-1)/k!. - Vladeta Jovovic, Oct 17 2007

a(n) ~ exp(2)/(exp(1)-1) * n^(n-1). - Vaclav Kotesovec, Nov 27 2012

E.g.f.: W(0)/(2-2*x) , where W(k) = 1 + 1/( 1 - x*(k+2)^k/( x*(k+2)^k + (k+1)^k/W(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Aug 19 2013

From Seiichi Manyama, May 01 2023: (Start)

E.g.f.: exp(-LambertW(-x))/(1-x).

a(0) = 1; a(n) = n*a(n-1) + (n+1)^(n-1). (End)

Mathematica

CoefficientList[Series[LambertW[-x]/(x*(x-1)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Nov 27 2012 *)

Prog

(PARI) my(x='x+O('x^50)); Vec(serlaplace(lambertw(-x)/(x*(x-1)))) \\ G. C. Greubel, Nov 08 2017

Crossrefs

Cf. A277506.

Sequence in context: A001028 A116481 A367494 * A195068 A342412 A196916

Adjacent sequences: A102740 A102741 A102742 * A102744 A102745 A102746

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 08 2005

Status

approved