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A087137
a(n) is the number of permutations in the symmetric group S_n that contain an odd cycle.
4
0, 1, 1, 6, 15, 120, 495, 5040, 29295, 362880, 2735775, 39916800, 370945575, 6227020800, 68916822975, 1307674368000, 16813959537375, 355687428096000, 5214921734397375, 121645100408832000, 2004231846526284375, 51090942171709440000, 934957186489800849375
OFFSET
0,4
LINKS
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.
MATHEMATICA
CoefficientList[Series[1/(1-x)-1/Sqrt[1-x^2], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Sep 21 2014 *)
PROG
(PARI) x='x+O('x^33); concat(0, Vec(serlaplace(1/(1-x)-1/sqrt(1-x^2)))) \\ Michel Marcus, Sep 21 2014
CROSSREFS
Sequence in context: A213873 A372990 A219771 * A056317 A129421 A013227
KEYWORD
nonn
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 18 2003
EXTENSIONS
Formulae and more terms from Vladeta Jovovic, Oct 31 2003
Two more terms from Michel Marcus, Sep 21 2014
STATUS
approved