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A130275
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Number of degree-n permutations such that number of cycles of size 2k is odd (or zero) for every k.
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0
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1, 1, 2, 6, 21, 105, 675, 4725, 35805, 322245, 3236625, 35602875, 425872755, 5536345815, 77347084815, 1160206272225, 18403556596425, 312860462139225, 5643104418376425, 107218983949152075, 2136610763952639975
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| E.g.f.: sqrt((1+x)/(1-x))*Product_{k>0} (1+sinh(x^(2*k)/(2*k))).
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EXAMPLE
| a(4)=21 because only the following three degree-4 permutations do not qualify: (12)(34), (13)(24) and (14)(23).
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MAPLE
| g:=sqrt((1+x)/(1-x))*(product(1+sinh(x^(2*k)/(2*k)), k=1..30)): gser:=series(g, x=0, 25): seq(factorial(n)*coeff(gser, x, n), n=0..20); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 24 2007
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CROSSREFS
| Cf. A003483, A006950, A015128, A102759, A130126, A131942, A130219-A130223.
Sequence in context: A020091 A008987 A079129 * A156808 A076324 A076325
Adjacent sequences: A130272 A130273 A130274 * A130276 A130277 A130278
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 06 2007
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 24 2007
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