A277466 E.g.f.: -log(1-x)/(1+LambertW(-x)).

0, 1, 3, 17, 146, 1684, 24294, 419383, 8412760, 192078864, 4914973770, 139265564723, 4327699948956, 146323675764044, 5347193667136398, 210005149832116455, 8820722263274822992, 394546588041904397184, 18723398414958791004690, 939550079246853331267203

Offset: 0

Author

Vaclav Kotesovec, Oct 16 2016

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..385

Crossrefs

Cf. A000312, A086331, A277465.

Programs

Mathematica

CoefficientList[Series[-Log[1-x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
Flatten[{0, Table[(n-1)! + n!*Sum[k^k/(k!*(n-k)), {k, 1, n-1}], {n, 1, 25}]}] (* Vaclav Kotesovec, Oct 28 2016 *)

PARI

x='x+O('x^50); concat([0], Vec(serlaplace(-log(1-x)/(1 + lambertw(-x))))) \\ G. C. Greubel, Nov 07 2017

Formula

a(n) ~ -log(1-exp(-1)) * n^n.