A087639 E.g.f.: Product_{m >= 1} (1+x^(2*m)/(2*m)) (even powers only).

1, 1, 6, 210, 8400, 740880, 88814880, 15217282080, 3319002086400, 992431440000000, 351841557779712000, 156995673442223616000, 82429416503416958976000, 52017974139195896832000000, 37547796668359538444083200000, 31987697744989345038846566400000

Offset: 0

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 06 2003

Keywords

• nonn

Comments

Number of permutations of 2*n elements with distinct cycle lengths and without odd cycles. - Vladeta Jovovic, Aug 17 2004

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..225

Crossrefs

Cf. A007838, A007841, A088994, A294506, A305199, A309319.

Programs

Maple

b:= proc(n, i) option remember; `if`((i/2)*(i/2+1)n, 0, (i-1)!*
       b(n-i, i-2)*binomial(n, i))))
    end:
a:= n-> b(2*n$2):
seq(a(n), n=0..17);  # Alois P. Heinz, Nov 01 2017

Mathematica

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 *)

Formula

a(n) ~ 2*exp(-gamma/2) * (2*n)! / (Pi*sqrt(n)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 23 2019

Extensions

More terms from Christian G. Bower, Jan 06 2006