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 A186767 Number of permutations of {1,2,...,n} having no nonincreasing odd cycles. 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)
 1, 1, 2, 5, 20, 77, 472, 2585, 21968, 157113, 1724064, 15229645, 204738624, 2151199429, 34194201472, 416221515169, 7631627843840, 105565890206193, 2192501224174080, 33962775502534165, 787900686999286784, 13509825183288167869 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) = A186766(n,0). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..450 FORMULA E.g.f.: g(z) = exp(sinh z)/sqrt(1-z^2). EXAMPLE a(3)=5 because we have (1)(2)(3), (1)(23), (12)(3), (13)(2), and (123). MAPLE g := exp(sinh(z))/sqrt(1-z^2): gser := series(g, z = 0, 27): seq(factorial(n)*coeff(gser, z, n), n = 0 .. 21); # second Maple program: a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*       binomial(n-1, j-1)*`if`(j::even, (j-1)!, 1), j=1..n))     end: seq(a(n), n=0..25);  # Alois P. Heinz, Apr 13 2017 MATHEMATICA a[n_] := a[n] = If[n==0, 1, Sum[a[n-j]*Binomial[n-1, j-1]*If[EvenQ[j], (j-1)!, 1], {j, 1, n}]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 18 2017, after Alois P. Heinz *) CROSSREFS Cf. A186761, A186762, A186763, A186764, A186765, A186766, A186769, A186770. Sequence in context: A221678 A297350 A027041 * A009737 A280624 A008983 Adjacent sequences:  A186764 A186765 A186766 * A186768 A186769 A186770 KEYWORD nonn AUTHOR Emeric Deutsch, Feb 27 2011 STATUS approved

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Last modified January 25 02:01 EST 2022. Contains 350565 sequences. (Running on oeis4.)