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

Author

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

Keywords

• nonn

Links

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

Crossrefs

Cf. A059838, A001818.

Programs

Mathematica

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

PARI

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

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.

Extensions

Formulae and more terms from Vladeta Jovovic, Oct 31 2003

Two more terms from Michel Marcus, Sep 21 2014