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A131526
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Number of degree-n permutations such that number of cycles of size 2k is even (or zero) and number of cycles of size 2k-1 is odd (or zero), for every k.
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0
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1, 1, 0, 3, 11, 40, 184, 1036, 12949, 88488, 807008, 7362586, 113572183, 1238477032, 15630890560, 228998728050, 4141605806441, 62222251093216, 1030119451142656, 19050688698470434, 412037845709792107, 8102391640556570616
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| E.g.f.: Product(1+sinh(x^(2*k-1)/(2*k-1)),k=1..infinity)*Product(cosh(x^(2*k)/(2*k)),k=1..infinity).
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EXAMPLE
| a(4)=11 because we have (1)(234), (1)(243), (123)(4), (124)(3), (132)(4), (134)(2), (142)(3), (143)(2), (12)(34), (13)(24) and (14)(23).
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MAPLE
| g:=(product(1+sinh(x^(2*k-1)/(2*k-1)), k=1..40))*(product(cosh(x^(2*k)/(2*k)), k=1..40)): gser:=series(g, x=0, 25); seq(factorial(n)*coeff(gser, x, n), n=0..21); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 28 2007
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CROSSREFS
| Sequence in context: A149063 A149064 A149065 * A073622 A181863 A075276
Adjacent sequences: A131523 A131524 A131525 * A131527 A131528 A131529
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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), Aug 28 2007
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