A289953 Number of permutations of [n] having exactly five nontrivial cycles.

945, 45045, 1344420, 33093060, 745860115, 16201119935, 348820952480, 7567361882080, 167057902281270, 3775807346835342, 87699348621850680, 2098002630307972920, 51760647309783259386, 1317835530989933266850, 34632875559239201852608, 939407586052413176727424

Offset: 10

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 = 10..450
• Wikipedia, Permutation

Crossrefs

Column k=5 of A136394.

Programs

Mathematica

Drop[Range[0, 30]! CoefficientList[Series[(-Log[1 - x] - x)^5 / 5! Exp[x], {x, 0, 30}], x], 10] (* Vincenzo Librandi, Jul 23 2017 *)

Formula

E.g.f.: (-log(1-x)-x)^5/5!*exp(x).