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Search: id:A134988
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| A134988 |
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Number of formal expessions obtained by applying iterated binary brackets to n indexed symbols x_1, ...,x_n such that: 1) each symbol appears exactly once; 2) the smallest index inside a bracket appears on the left hand side, and the largest index appears on the right hand side; 3) the outer bracket is the only bracket such that its set of indices is a sequence of consecutive integers. |
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+0
1
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| 1, 0, 1, 4, 22, 144, 1089, 9308, 88562, 927584, 10603178, 131368648, 1753970380, 25112732512, 383925637137, 6243618722124, 107644162715098, 1961478594977856, 37671587406585006
(list; graph; listen)
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OFFSET
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2,4
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COMMENT
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a(n) = number of generators in arity n of the operad Lie, when considered as a free non-symmetric operad.
a(n) = (1/e)*(1-3/n-5/(2n^2)+O(1/n^3))
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LINKS
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P. Salvatore and R. Tauraso, The Operad Lie is Free, arXiv:math.QA/0802.3010.
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FORMULA
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a(2)=1, a(n)=sum_{k=2..n-2}((k+1)*a(k+1)+a(k))*a(n-k), n>2; G.f.: A(x)=x-series_reversion(x*F(x)); where F(x) is the g.f. of the factorials (A000142).
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CROSSREFS
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Cf. A075834.
Sequence in context: A045744 A104991 A027391 this_sequence A081002 A057834 A121394
Adjacent sequences: A134985 A134986 A134987 this_sequence A134989 A134990 A134991
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KEYWORD
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nonn
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AUTHOR
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Paolo Salvatore and Roberto Tauraso (tauraso(AT)axp.mat.uniroma2.it), Feb 05 2008, Feb 22 2008
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