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A087137 a(n) is the number of permutations in the symmetric group S_n that contain an odd cycle. 4

%I

%S 0,1,1,6,15,120,495,5040,29295,362880,2735775,39916800,370945575,

%T 6227020800,68916822975,1307674368000,16813959537375,355687428096000,

%U 5214921734397375,121645100408832000,2004231846526284375,51090942171709440000,934957186489800849375

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

%H Alois P. Heinz, <a href="/A087137/b087137.txt">Table of n, a(n) for n = 0..450</a>

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

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

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

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

%Y Cf. A059838, A001818.

%K nonn

%O 0,4

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

%E Formulae and more terms from _Vladeta Jovovic_, Oct 31 2003

%E Two more terms from _Michel Marcus_, Sep 21 2014

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Last modified April 22 08:06 EDT 2019. Contains 322329 sequences. (Running on oeis4.)