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Search: id:A145886
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| A145886 |
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Number of excedances in all odd permutations of {1,2,...,n} with no fixed points. |
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+0
4
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| 0, 1, 0, 12, 50, 405, 3234, 29680, 300348, 3337425, 40382540, 528644556, 7445076990, 112248853717, 1803999433950, 30788257007040, 556112892188504, 10598857474652865, 212565974908314168, 4475073155964510700
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n)=Sum(k*A145880(n,k),k=1..n-1) (n>=2).
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REFERENCES
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R. Mantaci and F. Rakotondrajao, Exceedingly deranging!, Advances in Appl. Math., 30 (2003), 177-188.
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FORMULA
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E.g.f.=(1/4)*z^2*(2-2z+z^2)*exp(-z)/(1-z)^2.
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EXAMPLE
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a(4)=12 because the odd derangements of {1,2,3,4} are 4123, 3142, 4312, 2413, 2341 and 3421, having 1, 2, 2, 2, 3 and 2, excedances, respectively.
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MAPLE
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G:=(1/4)*z^2*(2-2*z+z^2)*exp(-z)/(1-z)^2: Gser:=series(G, z=0, 30): seq(factorial(n)*coeff(Gser, z, n), n=1..21);
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CROSSREFS
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A145880, A145881, A145887
Sequence in context: A063491 A083559 A051797 this_sequence A166776 A115680 A066757
Adjacent sequences: A145883 A145884 A145885 this_sequence A145887 A145888 A145889
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 06 2008
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