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%I #23 Jan 28 2022 06:21:29
%S 1,1,1,3,18,90,480,3360,27720,249480,2479680,27276480,327650400,
%T 4259455200,59623724160,894355862400,14309953257600,243269205379200,
%U 4378836875212800,83197900629043200,1663958347802150400,34943125303845158400,768748742605299456000
%N Number of permutations in the symmetric group S_n that have even number of transpositions in their cycle decomposition.
%H Vincenzo Librandi, <a href="/A088336/b088336.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: (exp(-x^2)+1)/(1-x)/2. - _Vladeta Jovovic_, Nov 09 2003
%F a(n) ~ n! * (1+exp(-1))/2. - _Vaclav Kotesovec_, Oct 08 2013
%t 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 *)
%o (PARI) x='x+O('x^50); Vec(serlaplace((exp(-x^2)+1)/(1-x)/2)) \\ _G. C. Greubel_, Aug 20 2017
%Y Cf. A000142, A062282, A088506.
%K nonn
%O 0,4
%A Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 07 2003
%E More terms from _Robert G. Wilson v_, May 04 2013
%E a(0) = 1 prepended by _Alois P. Heinz_, Jun 14 2015
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