A060307 Number of degree-4n permutations without odd cycles and such that number of cycles of size 2k is even (or zero) for every k.

1, 3, 1365, 8534295, 204893714025, 15735481638151275, 2760485970394430603325, 1006427270776555103089989375, 659316841888260316767029819420625, 740198799422691022278446846884066321875, 1306298536067264588818106780684613899555353125

Offset: 0

Author

Vladeta Jovovic, Mar 28 2001, Aug 10 2007

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A003483.

Cf. A013302.

Programs

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
      `if`(j=0 or irem(i, 2)=0 and irem(j, 2)=0, multinomial(n,
       n-i*j, i$j)*(i-1)!^j/j!*b(n-i*j, i-1), 0), j=0..n/i)))
    end:
a:= n-> b(4*n$2):
seq(a(n), n=0..15);  # Alois P. Heinz, Mar 09 2015

Mathematica

nn = 40; Select[Range[0, nn]! CoefficientList[Series[Product[Cosh[x^(2 i)/(2 i)], {i, 1, nn}], {x, 0, nn}], x], # > 0 &] (* Geoffrey Critzer, Jan 16 2012 *)

Formula

E.g.f.: Product_{k >= 1} cosh x^(2k)/(2k).