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