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A131525
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Number of degree-2n permutations such that number of cycles of size 2k is odd (or zero) and number of cycles of size 2k-1 is even (or zero), for every k.
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0
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1, 2, 13, 371, 17389, 1369057, 168362459, 28396593031, 6237698137129, 1823043651343241, 654314519766396223, 288203550242534470051, 151792464548141462268029, 95104739612472479469277141
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| E.g.f.: Product(1+sinh(x^(2*k)/(2*k)),k=1..infinity)*Product(cosh(x^(2*k-1)/(2*k-1)),k=1..infinity).
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EXAMPLE
| a(2)=13 because we have (1)(2)(3)(4), six permutations of type (p)(q)(rs) and six permutations of type (pqrs).
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MAPLE
| g:=product((1+sinh(x^(2*k)/(2*k)))*cosh(x^(2*k-1)/(2*k-1)), k=1..25): gser:= series(g, x=0, 30): seq(factorial(2*n)*coeff(gser, x, 2*n), n=0..13); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 04 2007
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CROSSREFS
| Sequence in context: A013106 A134485 A075620 * A082751 A120935 A015183
Adjacent sequences: A131522 A131523 A131524 * A131526 A131527 A131528
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 25 2007
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 04 2007
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