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 A186768 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)
 0, 0, 0, 1, 4, 43, 258, 2525, 20200, 222119, 2221190, 28061889, 336742668, 4856656283, 67993187962, 1107076110629, 17713217770064, 322047491979087, 5796854855623566, 116542615962575753, 2330852319251515060, 51380800712458456259 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS a(n) = Sum(k*A186766(n,k), k>=0). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA 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 EXAMPLE 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. MAPLE 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); MATHEMATICA 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 *) CROSSREFS Cf. A186761, A186763, A186764, A186766, A186769, A184958. Sequence in context: A296683 A297649 A186678 * A130545 A027311 A198205 Adjacent sequences: A186765 A186766 A186767 * A186769 A186770 A186771 KEYWORD nonn AUTHOR Emeric Deutsch, Feb 27 2011 EXTENSIONS Typo in e.g.f. corrected by Vaclav Kotesovec, Oct 07 2013 STATUS approved

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Last modified March 25 00:24 EDT 2023. Contains 361511 sequences. (Running on oeis4.)