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Search: id:A130276
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| A130276 |
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Number of degree-2n permutations such that 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, 16, 416, 20224, 1645312, 196388864, 33279311872, 7427338829824, 2151276556845056, 771086221948223488, 340572557390992900096, 179222835344084459061248, 112158801651454395931426816
(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.: 1/sqrt(1-x^2)*Product_{k>0} cosh(x^(2*k-1)/(2*k-1)).
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EXAMPLE
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a(2)=16 because there are 8 permutations that do not qualify: (1)(234), (1)(243), (123)(4), (124)(3), (132)(4), (134)(2), (142)(3), and (143)(2).
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MAPLE
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g:=(product(cosh(x^(2*k-1)/(2*k-1)), k=1..30))/sqrt(1-x^2): 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), Aug 24 2007
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CROSSREFS
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Cf. A003483, A006950, A015128, A102759, A130126, A131942, A130219-A130223.
Adjacent sequences: A130273 A130274 A130275 this_sequence A130277 A130278 A130279
Sequence in context: A009613 A012388 A012752 this_sequence A027871 A009397 A009700
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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 06 2007
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 24 2007
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