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Search: id:A130278
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| A130278 |
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Number of degree-n permutations such that number of cycles of size 2k-1 is odd (or zero) for every k. |
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+0
1
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| 1, 1, 1, 6, 17, 100, 529, 3766, 31121, 276984, 2755553, 29665306, 364627801, 4639937380, 64952094401, 973467571350, 15750475301921, 264870218828656, 4759194994114369, 90124395399063730, 1812001488739061417
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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E.g.f.: 1/sqrt(1-x^2)*Product_{k>0} (1+sinh(x^(2*k-1)/(2*k-1))).
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EXAMPLE
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a(4)=17 because only the following 7 permutations do not qualify: (1)(2)(3)(4), (1)(2)(34), (1)(23)(4), (1)(24)(3), (12)(3)(4), (13)(2)(4) and (14)(2)(3).
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MAPLE
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g:=(product(1+sinh(x^(2*k-1)/(2*k-1)), k=1..30))/sqrt(1-x^2): 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
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Cf. A003483, A006950, A015128, A102759, A130126, A131942, A130219-A130223.
Adjacent sequences: A130275 A130276 A130277 this_sequence A130279 A130280 A130281
Sequence in context: A123189 A047156 A154494 this_sequence A024080 A099436 A077022
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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.rs), 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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