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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. 5
1, 3, 1365, 8534295, 204893714025, 15735481638151275, 2760485970394430603325, 1006427270776555103089989375, 659316841888260316767029819420625, 740198799422691022278446846884066321875, 1306298536067264588818106780684613899555353125 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Mar 28 2001, Aug 10 2007
STATUS
approved

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Last modified May 25 16:13 EDT 2024. Contains 372800 sequences. (Running on oeis4.)