A087137 a(n) is the number of permutations in the symmetric group S_n that contain an odd cycle.

0, 1, 1, 6, 15, 120, 495, 5040, 29295, 362880, 2735775, 39916800, 370945575, 6227020800, 68916822975, 1307674368000, 16813959537375, 355687428096000, 5214921734397375, 121645100408832000, 2004231846526284375, 51090942171709440000, 934957186489800849375

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..450

Formula

E.g.f.: 1/(1-x)-1/sqrt(1-x^2).

If n is odd then a(n) = n! else a(n) = n!-((n-1)!!)^2.

Mathematica

CoefficientList[Series[1/(1-x)-1/Sqrt[1-x^2], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Sep 21 2014 *)

Prog

(PARI) x='x+O('x^33); concat(0, Vec(serlaplace(1/(1-x)-1/sqrt(1-x^2)))) \\ Michel Marcus, Sep 21 2014

Crossrefs

Cf. A059838, A001818.

Sequence in context: A213873 A372990 A219771 * A056317 A129421 A013227

Adjacent sequences: A087134 A087135 A087136 * A087138 A087139 A087140

Keyword

nonn

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 18 2003

Extensions

Formulae and more terms from Vladeta Jovovic, Oct 31 2003

Two more terms from Michel Marcus, Sep 21 2014

Status

approved