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
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..100
Programs
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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).
Comments