A273434 Number of endofunctions on [n] with exactly three cycles.

1, 18, 305, 5595, 113974, 2581964, 64727522, 1783995060, 53705023251, 1755078270264, 61920105083187, 2346728722199680, 95117694573257784, 4106779625155078528, 188206877039146217476, 9125798298446360109312, 466820173490890114763781, 25126459591455539907002880

Offset: 3

Author

Alois P. Heinz, May 22 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..386

Crossrefs

Column k=3 of A060281.

Programs

Mathematica

Drop[CoefficientList[Series[-1/6 * Log[1+LambertW[-x]]^3, {x, 0, 20}], x] * Range[0, 20]!, 3] (* Vaclav Kotesovec, Nov 01 2016 *)

PARI

x='x+O('x^30); Vec(serlaplace(-log(1+lambertw(-x))^3/6)) \\ G. C. Greubel, Aug 30 2018

Formula

E.g.f.: -1/6 * log(1+LambertW(-x))^3.

a(n) ~ n^(n-1/2) * sqrt(2*Pi) * (log(n))^2 / 16 * (1 + 2*(gamma - log(2))/log(n) + (gamma^2 - 2*log(2)*gamma + log(2)^2 - Pi^2/6)/log(n)^2), where gamma is the Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Nov 01 2016