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

0,4

Links

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

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

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 *)

Prog

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

Crossrefs

Cf. A000142, A062282, A088506.

Sequence in context: A006568 A181955 A147518 * A133594 A272492 A092691

Adjacent sequences: A088333 A088334 A088335 * A088337 A088338 A088339

Keyword

nonn

Author

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

Extensions

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

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

Status

approved