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Search: id:A145887
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| A145887 |
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Number of excedances in all even permutations of {1,2,...,n} with no fixed points. |
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+0
4
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| 0, 0, 3, 6, 60, 390, 3255, 29652, 300384, 3337380, 40382595, 528644490, 7445077068, 112248853626, 1803999434055, 30788257006920, 556112892188640, 10598857474652712, 212565974908314339, 4475073155964510510
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OFFSET
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1,3
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COMMENT
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a(n)=Sum(k*A145881(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-z)*exp(-z)/(1-z)^2.
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EXAMPLE
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a(4)=6 because the even derangements of {1,2,3,4} are 3412, 2143 and 4321, having 2, 2 and 2, excedances, respectively.
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MAPLE
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G:=(1/4)*z^3*(2-z)*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, A145886
Sequence in context: A058161 A012877 A103066 this_sequence A137123 A137133 A137137
Adjacent sequences: A145884 A145885 A145886 this_sequence A145888 A145889 A145890
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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 07 2008
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