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%I #20 Jul 27 2019 02:36:57
%S 1,1,6,210,8400,740880,88814880,15217282080,3319002086400,
%T 992431440000000,351841557779712000,156995673442223616000,
%U 82429416503416958976000,52017974139195896832000000,37547796668359538444083200000,31987697744989345038846566400000
%N E.g.f.: Product_{m >= 1} (1+x^(2*m)/(2*m)) (even powers only).
%C Number of permutations of 2*n elements with distinct cycle lengths and without odd cycles. - _Vladeta Jovovic_, Aug 17 2004
%H Alois P. Heinz, <a href="/A087639/b087639.txt">Table of n, a(n) for n = 0..225</a>
%F a(n) ~ 2*exp(-gamma/2) * (2*n)! / (Pi*sqrt(n)), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Jul 23 2019
%p b:= proc(n, i) option remember; `if`((i/2)*(i/2+1)<n, 0,
%p `if`(n=0, 1, b(n,i-2)+`if`(i>n, 0, (i-1)!*
%p b(n-i, i-2)*binomial(n, i))))
%p end:
%p a:= n-> b(2*n$2):
%p seq(a(n), n=0..17); # _Alois P. Heinz_, Nov 01 2017
%t nmax = 20; Table[(CoefficientList[Series[Product[1 + x^(2*k)/(2*k), {k, 1, 2*nmax}], {x, 0, 2*nmax}], x]*Range[0, 2*nmax]!)[[2*n + 1]], {n, 0, nmax}] (* _Vaclav Kotesovec_, Jul 23 2019 *)
%Y Cf. A007838, A007841, A088994, A294506, A305199, A309319.
%K nonn
%O 0,3
%A Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 06 2003
%E More terms from _Christian G. Bower_, Jan 06 2006
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