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A186768
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Number of nonincreasing odd 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 odd if it has an odd number of entries.
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4
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0, 0, 0, 1, 4, 43, 258, 2525, 20200, 222119, 2221190, 28061889, 336742668, 4856656283, 67993187962, 1107076110629, 17713217770064, 322047491979087, 5796854855623566, 116542615962575753, 2330852319251515060, 51380800712458456259
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OFFSET
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0,5
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COMMENTS
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a(n) = Sum(k*A186766(n,k), k>=0).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
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FORMULA
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E.g.f.: g(z)=[log((1+z)/(1-z))-2sinh(z)]/(2(1-z)).
a(n) ~ n!/2 * (log(2*n) + gamma - exp(1) + exp(-1)), where gamma is the Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Oct 07 2013
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EXAMPLE
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a(3)=1 because in (1)(2)(3), (1)(23), (12)(3), (13)(2), (123), and (132) we have a total of 0+0+0+0+0+1 =1 increasing odd cycles.
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MAPLE
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g := ((ln((1+z)/(1-z))-2*sinh(z))*1/2)/(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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CoefficientList[Series[(Log[(1+x)/(1-x)]-2*Sinh[x])/(2*(1-x)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 07 2013 *)
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CROSSREFS
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Cf. A186761, A186763, A186764, A186766, A186769, A184958.
Sequence in context: A296683 A297649 A186678 * A130545 A027311 A198205
Adjacent sequences: A186765 A186766 A186767 * A186769 A186770 A186771
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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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EXTENSIONS
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Typo in e.g.f. corrected by Vaclav Kotesovec, Oct 07 2013
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STATUS
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approved
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