cp's OEIS Frontend

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) . A cycle is said to be odd if it has an odd number of entries.

%I A186767 #11 May 18 2017 10:14:20
%S A186767 1,1,2,5,20,77,472,2585,21968,157113,1724064,15229645,204738624,
%T A186767 2151199429,34194201472,416221515169,7631627843840,105565890206193,
%U A186767 2192501224174080,33962775502534165,787900686999286784,13509825183288167869
%N 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.
%C A186767 a(n) = A186766(n,0).
%H A186767 Alois P. Heinz, <a href="/A186767/b186767.txt">Table of n, a(n) for n = 0..450</a>
%F A186767 E.g.f.: g(z) = exp(sinh z)/sqrt(1-z^2).
%e A186767 a(3)=5 because we have (1)(2)(3), (1)(23), (12)(3), (13)(2), and (123).
%p A186767 g := exp(sinh(z))/sqrt(1-z^2): gser := series(g, z = 0, 27): seq(factorial(n)*coeff(gser, z, n), n = 0 .. 21);
%p A186767 # second Maple program:
%p A186767 a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*
%p A186767       binomial(n-1, j-1)*`if`(j::even, (j-1)!, 1), j=1..n))
%p A186767     end:
%p A186767 seq(a(n), n=0..25);  # _Alois P. Heinz_, Apr 13 2017
%t A186767 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}]];
%t A186767 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, May 18 2017, after _Alois P. Heinz_ *)
%Y A186767 Cf. A186761, A186762, A186763, A186764, A186765, A186766, A186769, A186770.
%K A186767 nonn
%O A186767 0,3
%A A186767 _Emeric Deutsch_, Feb 27 2011