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

3,2

Links

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

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

Mathematica

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

Prog

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

Crossrefs

Column k=3 of A060281.

Sequence in context: A228605 A193317 A161599 * A083451 A162804 A097831

Adjacent sequences: A273431 A273432 A273433 * A273435 A273436 A273437

Keyword

nonn

Author

Alois P. Heinz, May 22 2016

Status

approved