A186770 Number of permutations of {1,2,...,n} having no nonincreasing even 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, 6, 19, 95, 451, 3157, 21092, 189828, 1660351, 18263861, 197541565, 2568040345, 33029787974, 495446819610, 7377279473779, 125413751054243, 2120559951767503, 40290639083582557, 762353357154540584, 16009420500245352264

Offset: 0

Author

Emeric Deutsch, Feb 27 2011

Keywords

• nonn

Comments

a(n) = A186769(n,0).

Examples

			a(4)=19 because among the 24 permutations of {1,2,3,4} only (1243), (1324), (1342), (1423), and (1432) have nonincreasing even cycles.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A186761, A186762, A186764, A186765, A186766, A186767, A186769.

Programs

Maple

g := exp(cosh(z)-1)*sqrt((1+z)/(1-z)): 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::odd, (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[OddQ[j], (j-1)!, 1], {j, 1, n}]];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 18 2017, after Alois P. Heinz *)

Formula

E.g.f.: g(z) = exp(cosh z - 1)*sqrt((1+z)/(1-z)).