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Search: id:A102594
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| A102594 |
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Number of noncrossing trees with n edges in which no border edges emanate from the root. |
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+0
3
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| 1, 0, 0, 1, 7, 42, 245, 1428, 8379, 49588, 296010, 1781325, 10798788, 65900296, 404565252, 2496994136, 15486165555, 96464124648, 603262881620, 3786268349115, 23842082904255, 150586208376450, 953736669989985
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OFFSET
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0,5
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COMMENT
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Column 0 of A102593.
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REFERENCES
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M. Noy, Enumeration of noncrossing trees on a circle, Discrete Math.180, 1998, 301-313.
P. Flajolet and M. Noy, Analytic combinatorics of non-crossing configurations, Discrete Math., 204, 1999, 203-229.
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FORMULA
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a(n)=7/3*(n-1)*(n-2)*binomial(3*n, n)/(3*n-1)/(2*n+1)/(3*n-2) for n>0; a(0)=1. G.f.=g(1+z-2zg), where g=1+zg^3 is the g.f. of the ternary numbers (A001764).
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EXAMPLE
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a(2)=0 because in all the three noncrossing trees with 2 edges, namely, /_, /\, and _\, the root (=the top vertex) is incident with at least one border edge.
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MAPLE
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a:=n->7/3*(n-1)*(n-2)*binomial(3*n, n)/(3*n-1)/(2*n+1)/(3*n-2): 1, seq(a(n), n=1..25);
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CROSSREFS
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Cf. A001764, A102593.
Sequence in context: A050152 A030240 A054890 this_sequence A053142 A094168 A003949
Adjacent sequences: A102591 A102592 A102593 this_sequence A102595 A102596 A102597
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 22 2005
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