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A087639 E.g.f.: Product_{m >= 1} (1+x^(2*m)/(2*m)) (even powers only). 5
1, 1, 6, 210, 8400, 740880, 88814880, 15217282080, 3319002086400, 992431440000000, 351841557779712000, 156995673442223616000, 82429416503416958976000, 52017974139195896832000000, 37547796668359538444083200000, 31987697744989345038846566400000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

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

MAPLE

b:= proc(n, i) option remember; `if`((i/2)*(i/2+1)<n, 0,

      `if`(n=0, 1, b(n, i-2)+`if`(i>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 *)

CROSSREFS

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

Sequence in context: A029549 A183252 A183287 * A028350 A238685 A099788

Adjacent sequences:  A087636 A087637 A087638 * A087640 A087641 A087642

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

More terms from Christian G. Bower, Jan 06 2006

STATUS

approved

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Last modified April 22 10:58 EDT 2021. Contains 343174 sequences. (Running on oeis4.)