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