A060918 Expansion of e.g.f.: exp((-1)^k/k*LambertW(-x)^k)/(k-1)!, k=4.

1, 20, 360, 6860, 143570, 3321864, 84756000, 2372001720, 72384192540, 2394775746220, 85443353291296, 3271908306712500, 133893717061821080, 5832748749666611920, 269542701201588099840, 13172225935626444660144, 678788199609330554538000, 36790272488566573278647940

Offset: 4

Author

Vladeta Jovovic, Apr 10 2001

Keywords

• easy
• nonn

Comments

a(n) = A243098(n,4)/6. - Alois P. Heinz, Aug 19 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 4..200

Crossrefs

Cf. A057817, A060917, A243098.

Programs

Mathematica

CoefficientList[Series[E^(1/4*LambertW[-x]^4)/6, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Nov 27 2012 *)

PARI

x='x+O('x^30); Vec(serlaplace(exp(lambertw(-x)^4/4)/3! - 1/3!)) \\ 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=4.

a(n) ~ 1/6*exp(1/4)*n^(n-1). - Vaclav Kotesovec, Nov 27 2012