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Search: id:A131525
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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
1
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| 1, 2, 13, 371, 17389, 1369057, 168362459, 28396593031, 6237698137129, 1823043651343241, 654314519766396223, 288203550242534470051, 151792464548141462268029, 95104739612472479469277141
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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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
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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
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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
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Adjacent sequences: A131522 A131523 A131524 this_sequence A131526 A131527 A131528
Sequence in context: A013106 A134485 A075620 this_sequence A082751 A120935 A015183
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 25 2007
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 04 2007
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