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Search: id:A063083
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| A063083 |
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Number of permutations of n elements with an odd number of fixed points. |
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+0
8
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| 0, 1, 0, 4, 8, 56, 304, 2192, 17408, 156928, 1568768, 17257472, 207087616, 2692143104, 37689995264, 565349945344, 9045599092736, 153775184642048, 2767953323425792, 52591113145352192, 1051822262906519552
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OFFSET
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0,4
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FORMULA
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E.g.f.: sinh(x) * exp(-x)/(1-x). Asymptotic expression: a(n) ~ n! * (1 - 1/e^2)/2 i.e. as n goes to infinity the fraction for permutations that has an odd number of fixed points is about (1 - 1/e^2)/2 = 0.432332...
a(n) = n! - A062282(n) = n! - sum k=0 ... [n/2] sum l=0...n-2k (-1)^l * n!/((2k)! * l!)
Recurrence: a(n) = n*a(n-1)+(-2)^(n-1). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 11 2003
More generally, e.g.f. for number of degree-n permutations with an odd number of k-cycles is sinh(x^k/k)*exp(-x^k/k)/(1-x). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 31 2006
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CROSSREFS
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Cf. A062282.
Sequence in context: A056397 A123106 A123288 this_sequence A120777 A091095 A075787
Adjacent sequences: A063080 A063081 A063082 this_sequence A063084 A063085 A063086
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KEYWORD
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nonn
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), Aug 05 2001
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EXTENSIONS
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More terms from Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 09 2001
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