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A087639
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E.g.f.: Product_{m >= 1} (1+x^(2*m)/(2*m)) (even powers only).
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5
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1, 1, 6, 210, 8400, 740880, 88814880, 15217282080, 3319002086400, 992431440000000, 351841557779712000, 156995673442223616000, 82429416503416958976000, 52017974139195896832000000, 37547796668359538444083200000, 31987697744989345038846566400000
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OFFSET
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0,3
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COMMENTS
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Number of permutations of 2*n elements with distinct cycle lengths and without odd cycles. - Vladeta Jovovic, Aug 17 2004
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LINKS
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FORMULA
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a(n) ~ 2*exp(-gamma/2) * (2*n)! / (Pi*sqrt(n)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 23 2019
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MAPLE
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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):
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 06 2003
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EXTENSIONS
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STATUS
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approved
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