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Search: id:A029767
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| 0, 1, 3, 14, 90, 744, 7560, 91440, 1285200, 20603520, 371226240, 7428153600, 163459296000, 3923502105600, 102017281766400, 2856571067750400, 85698439706880000, 2742370993410048000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Labeled octupi with n nodes.
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, pp. 12, 55, 409.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.1.5.
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 498
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 777
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FORMULA
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(n-1)!*(2^n-1). E.g.f.: log(1-x)-log(1-2*x).
In Maple notation, representation as an infinite sum: a(n)=sum((n+k)!/((k+1)!*2^k), k=0..infinity)/2, n=1, 2... Representation as n-th moment of a positive function on a positive half-axis: a(n)=int(x^n*1/2*exp(-x)/x*(2*exp(1/2*x)-2), x=0..infinity), n=1, 2... - Karol A. Penson (penson(AT)lptl.jussieu.fr), Oct 15 2002
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MAPLE
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with(combinat):seq((stirling1(j+1, 1)*(stirling2(j+2, 2))*(-1)^j), j=-1..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 30 2007
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CROSSREFS
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Sequence in context: A081005 A074518 A088789 this_sequence A120056 A125788 A101220
Adjacent sequences: A029764 A029765 A029766 this_sequence A029768 A029769 A029770
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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