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Search: id:A130263
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| A130263 |
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Number of degree-n permutations such that number of cycles of size k is odd (or zero) for every k. |
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+0
1
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| 1, 1, 1, 6, 14, 85, 529, 3451, 26816, 243909, 2507333, 26196841, 323194816, 4086482335, 57669014597, 864137455455, 13792308331616, 231648908415001, 4211676768746569, 79205041816808905, 1584565388341689032
(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.: Product_{k>0} (1+sinh(x^k/k)).
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EXAMPLE
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a(2)=1 because we have (12) ((1)(2) does not qualify). a(4)=14 because the following 10 permutations of 4 do not qualify: (1)(2)(3)(4), (14)(2)(3), (1)(24)(3), (1)(2)(34), (13)(2)(4), (13)(24), (1)(23)(4), (14)(23), (12)(3)(4) and (12)(34).
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MAPLE
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g:=product(1+sinh(x^k/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 24 2007
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CROSSREFS
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Cf. A055922, A130219, A130220.
Sequence in context: A059954 A139257 A056842 this_sequence A077401 A158965 A013314
Adjacent sequences: A130260 A130261 A130262 this_sequence A130264 A130265 A130266
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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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