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A219613
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E.g.f. tan(x/(1-x)).
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6
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0, 1, 2, 8, 48, 376, 3600, 40592, 525952, 7692928, 125303040, 2248366592, 44055035904, 935800603648, 21417131939840, 525346642337792, 13748654428323840, 382362034331877376, 11260657076602208256, 350082293087247269888, 11457214800338786713600
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OFFSET
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0,3
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COMMENTS
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Take each set partition of {1,2,...,n} into an odd number of blocks. Linearly order the elements within each block then form a "zag" permutation with the smallest element from each block. Here a "zag" permutation is a permutation a[1],a[2],...,a[k] such that a[1] < a[2] > a[3] < ... > a[k]. a(n) is the number of ways to order the blocks in accordance with each "zag" permutation.
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LINKS
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FORMULA
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E.g.f.: x/(1-x)/T(0), where T(k) = 4*k+1 - x^2/((4*k+3)*(1-x)^2 - x^2/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 30 2013
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EXAMPLE
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a(3) = 8: The set partitions of {1,2,3} into an odd number of blocks are {1,2,3} and {1}{2}{3}. There are 6 ways to linearly order the elements of {1,2,3}. There are 2 such ways to order the blocks of the set partition {1}{2}{3}: {1}{3}{2} and {2}{3}{1}. 6+2=8.
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MATHEMATICA
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nn=21; Range[0, nn]!CoefficientList[Series[Tan[x/(1-x)], {x, 0, nn}], x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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