A060917 Expansion of e.g.f.: exp((-1)^k/k*LambertW(-x)^k)/(k-1)!, k=3.

1, 12, 150, 2180, 36855, 715008, 15697948, 385300800, 10463945085, 311697869120, 10108450408914, 354630018043392, 13384651003544275, 540860323696035840, 23300648262667635960, 1066165291831917811712

Offset: 3

Author

Vladeta Jovovic, Apr 10 2001

Keywords

• easy
• nonn

Comments

a(n) = A243098(n,3)/2. - Alois P. Heinz, Aug 19 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 3..200

Crossrefs

Cf. A057817, A060918, A243098.

Programs

Mathematica

nn = 20; CoefficientList[Series[E^(-1/3*LambertW[-x]^3)/2, {x, 0, nn}], x]* Range[0, nn]! (* Vaclav Kotesovec, Nov 27 2012 *)

PARI

x='x+O('x^30); Vec(serlaplace(exp(-lambertw(-x)^3/3)/2 - 1/2)) \\ G. C. Greubel, Feb 19 2018

Formula

a(n) = (n-1)!/(k-1)!*Sum_{i=0..floor((n-k)/k)} 1/(i!*k^i)*n^(n-(i+1)*k)/(n-(i+1)*k)!, k=3.

a(n) ~ 1/2*exp(1/3)*n^(n-1). - Vaclav Kotesovec, Nov 27 2012