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A184958
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Number of nonincreasing even cycles in all permutations of {1,2,...,n}. A cycle (b(1), b(2), ...) is said to be increasing if, when written with its smallest element in the first position, it satisfies b(1)<b(2)<b(3)<... . A cycle is said to be even if it has an even number of entries.
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3
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0, 0, 0, 0, 5, 25, 269, 1883, 20103, 180927, 2172149, 23893639, 326640467, 4246326071, 65675585793, 985133786895, 17069814958319, 290186854291423, 5579050805341613, 106001965301490647, 2241684406438644939, 47075372535211543719
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OFFSET
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0,5
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COMMENTS
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a(n)=Sum(k*A186769(n,k), k>=0).
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LINKS
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Table of n, a(n) for n=0..21.
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FORMULA
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E.g.f.: g(z)=(1/2)[2(1-cosh z) - ln(1-z^2)]/(1-z).
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EXAMPLE
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a(4)=5 because the only permutations of {1,2,3,4} having nonincreasing even cycles are (1243), (1324), (1342), (1423), and (1432).
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MAPLE
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g := (1/2*(2*(1-cosh(z))-ln(1-z^2)))/(1-z): gser := series(g, z = 0, 27): seq(factorial(n)*coeff(gser, z, n), n = 0 .. 21);
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[1/2(2(1-Cosh[x])-Log[1-x^2])/(1-x), {x, 0, nn}], x]Range[0, nn]!] (* From Harvey P. Dale, Oct 22 2011 *)
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CROSSREFS
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Cf. A186761, A186763, A186764, A186766, A186768, A186769
Sequence in context: A005452 A143600 A209529 * A145076 A185063 A165656
Adjacent sequences: A184955 A184956 A184957 * A184959 A184960 A184961
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch, Feb 27 2011
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STATUS
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approved
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