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A009411
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Expansion of log(1+x)*cosh(log(1+x)).
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1
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0, 1, -1, 5, -24, 134, -870, 6474, -54432, 510768, -5294160, 60090480, -741407040, 9881421120, -141493322880, 2166467990400, -35323552051200, 611048958105600, -11178032634316800, 215604729694771200, -4373272831527936000
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OFFSET
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0,4
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COMMENTS
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|a(n)| = number of cycles in all permutations of [n] with odd number of cycles. - Vladeta Jovovic, Sep 06 2007
a(n) is a function of the harmonic numbers. - Gary Detlefs, Jul 13 2010
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LINKS
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Robert Israel, Table of n, a(n) for n = 0..411
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FORMULA
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a(n) = (-1)^(n+1)/2*(n!*H(n)-(n-2)!), n> 1, where H(n) = sum(1/k, k=1..n). - Gary Detlefs, Jul 13 2010
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MAPLE
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H:= n-> sum(1/k, k=1..n): seq((-1)^(n+1)/2*(n!*H(n)-(n-2)!), n = 2..20); # Gary Detlefs, Jul 13 2010
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MATHEMATICA
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Log[ 1+x ]*Cosh[ Log[ 1+x ] ]
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CROSSREFS
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Cf. A000254.
Sequence in context: A066118 A002709 A193668 * A080996 A020055 A256325
Adjacent sequences: A009408 A009409 A009410 * A009412 A009413 A009414
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KEYWORD
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sign,easy
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AUTHOR
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R. H. Hardin
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EXTENSIONS
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Extended with signs by Olivier Gérard, Mar 15 1997
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STATUS
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approved
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