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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)<b(2)<b(3)<... . A cycle is said to be odd if it has an odd number of entries. 4
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.)