A289956 Number of permutations of [n] having exactly eight nontrivial cycles.

2027025, 218243025, 13818229425, 680438103345, 29079209884725, 1141483113695925, 42556765607801445, 1539279211706361125, 54789078082648965055, 1938102614993339970175, 68612592434209034386175, 2443274471026078967051775, 87839862102761225799417075

Offset

16,1

Comments

A nontrivial cycle has size > 1.

Links

Alois P. Heinz, Table of n, a(n) for n = 16..450

Wikipedia, Permutation

Formula

E.g.f.: (log(1-x)+x)^8/8!*exp(x).

Mathematica

Drop[CoefficientList[Series[(Log[1 - x] + x)^8/8!*Exp[x] , {x, 0, 50}], x] * Table[k !, {k, 0, 50}] , 16] (* Indranil Ghosh, Jul 16 2017 *)

Prog

(PARI) x = 'x + O('x^30); Vec(serlaplace((-log(1-x)-x)^8/8!*exp(x))) \\ Michel Marcus, Jul 16 2017

Crossrefs

Column k=8 of A136394.

Sequence in context: A104441 A346515 A290037 * A263892 A163682 A045871

Adjacent sequences: A289953 A289954 A289955 * A289957 A289958 A289959

Keyword

nonn

Author

Alois P. Heinz, Jul 16 2017

Status

approved