A289957 Number of permutations of [n] having exactly nine nontrivial cycles.

34459425, 4583103525, 353553700500, 20941727706900, 1063956789420525, 49122916648430625, 2133284602385096160, 89095866141017736000, 3632887356673057858375, 146162134100332940264675, 5846991791902793693661500, 233881907399101905866222300

Offset: 18

Author

Alois P. Heinz, Jul 16 2017

Keywords

• nonn

Comments

A nontrivial cycle has size > 1.

Links

• Alois P. Heinz, Table of n, a(n) for n = 18..450
• Wikipedia, Permutation

Crossrefs

Column k=9 of A136394.

Programs

Mathematica

Drop[CoefficientList[Series[(-Log[1 - x] - x)^9/9!*Exp[x] , {x, 0, 50}], x] * Table[k !, {k, 0, 50}] , 18] (* Indranil Ghosh, Jul 16 2017 *)

PARI

x = 'x + O('x^30); Vec(serlaplace((-log(1-x)-x)^9/9!*exp(x))) \\ Michel Marcus, Jul 16 2017

Formula

E.g.f.: (-log(1-x)-x)^9/9!*exp(x).