cp's OEIS Frontend

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.

%I A060307 #14 Mar 09 2015 11:52:17
%S A060307 1,3,1365,8534295,204893714025,15735481638151275,
%T A060307 2760485970394430603325,1006427270776555103089989375,
%U A060307 659316841888260316767029819420625,740198799422691022278446846884066321875,1306298536067264588818106780684613899555353125
%N 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.
%H A060307 Alois P. Heinz, <a href="/A060307/b060307.txt">Table of n, a(n) for n = 0..100</a>
%F A060307 E.g.f.: Product_{k >= 1} cosh x^(2k)/(2k).
%p A060307 with(combinat):
%p A060307 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A060307       `if`(j=0 or irem(i, 2)=0 and irem(j, 2)=0, multinomial(n,
%p A060307        n-i*j, i$j)*(i-1)!^j/j!*b(n-i*j, i-1), 0), j=0..n/i)))
%p A060307     end:
%p A060307 a:= n-> b(4*n$2):
%p A060307 seq(a(n), n=0..15);  # _Alois P. Heinz_, Mar 09 2015
%t A060307 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 *)
%Y A060307 Cf. A003483.
%Y A060307 Cf. A013302.
%K A060307 easy,nonn
%O A060307 0,2
%A A060307 _Vladeta Jovovic_, Mar 28 2001, Aug 10 2007