A088336 Number of permutations in the symmetric group S_n that have even number of transpositions in their cycle decomposition.

1, 1, 1, 3, 18, 90, 480, 3360, 27720, 249480, 2479680, 27276480, 327650400, 4259455200, 59623724160, 894355862400, 14309953257600, 243269205379200, 4378836875212800, 83197900629043200, 1663958347802150400, 34943125303845158400, 768748742605299456000

Offset: 0

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 07 2003

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A000142, A062282, A088506.

Programs

Mathematica

mx = 21; Rest[ Range[0, mx]! CoefficientList[ Series[(Exp[-x^2] + 1)/(1 - x)/2, {x, 0, mx}], x]] (* Robert G. Wilson v, May 04 2013 *)

PARI

x='x+O('x^50); Vec(serlaplace((exp(-x^2)+1)/(1-x)/2)) \\ G. C. Greubel, Aug 20 2017

Formula

E.g.f.: (exp(-x^2)+1)/(1-x)/2. - Vladeta Jovovic, Nov 09 2003

a(n) ~ n! * (1+exp(-1))/2. - Vaclav Kotesovec, Oct 08 2013

Extensions

More terms from Robert G. Wilson v, May 04 2013

a(0) = 1 prepended by Alois P. Heinz, Jun 14 2015