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

0,2

Links

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

Formula

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

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 *)

Crossrefs

Cf. A003483.

Cf. A013302.

Sequence in context: A122389 A036066 A262516 * A119111 A233195 A219783

Adjacent sequences: A060304 A060305 A060306 * A060308 A060309 A060310

Keyword

easy,nonn

Author

Vladeta Jovovic, Mar 28 2001, Aug 10 2007

Status

approved