A289958 Number of permutations of [n] having exactly ten nontrivial cycles.

654729075, 105411381075, 9729928783575, 682187321190375, 40619713503218850, 2178070341434237250, 108946451099337101250, 5201416870471272701250, 240786076823686096077375, 10929696310323023478019775, 490470855046984824670532875, 21893162839119896036432594875

Offset

20,1

Comments

A nontrivial cycle has size > 1.

Links

Alois P. Heinz, Table of n, a(n) for n = 20..450

Wikipedia, Permutation

Formula

E.g.f.: (log(1-x)+x)^10/10!*exp(x).

Mathematica

Drop[CoefficientList[Series[(Log[1 - x] + x)^10/10!*Exp[x] , {x, 0, 50}], x] * Table[k!, {k, 0, 50}] , 20] (* Indranil Ghosh, Jul 16 2017 *)

Prog

(PARI) x = 'x + O('x^30); Vec(serlaplace((-log(1-x)-x)^10/10!*exp(x))) \\ Michel Marcus, Jul 16 2017

Crossrefs

Column k=10 of A136394.

Sequence in context: A307759 A271770 A290039 * A263894 A291550 A234071

Adjacent sequences: A289955 A289956 A289957 * A289959 A289960 A289961

Keyword

nonn

Author

Alois P. Heinz, Jul 16 2017

Status

approved