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Search: id:A062236
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| A062236 |
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Sum of the levels of all nodes in all noncrossing trees with n edges. |
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1
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| 1, 8, 58, 408, 2831, 19496, 133638, 913200, 6226591, 42387168, 288194424, 1957583712, 13286865060, 90126841064, 611029568078, 4140789069408, 28050809681679, 189964288098632, 1286119453570746, 8705397371980728
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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E. Deutsch and M. Noy, New statistics on non-crossing trees, in: Formal Power Series and Algebraic Combinatorics (Proceedings of the 12th International Conference, FPSAC'00, Moscow, Russia, 2000), pp. 667-676, Springer, Berlin, 2000.
P. Flajolet and M. Noy, Analytic combinatorics of non-crossing configurations, Discrete Math., 204, 203-229, 1999.
M. Noy, Enumeration of noncrossing trees on a circle, Discrete Math., 180, 301-313, 1998.
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FORMULA
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G.f.: g*(g-1)/(3-2*g)^2, where g=1+z^3g, g(0)=0 or g := 2*sin(arcsin(3*sqrt(3*z)/2)/3)/sqrt(3*z);
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MAPLE
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a := n->sum(2^(n-2-i)*(n-i)*(3*n-3*i-1)*binomial(3*n, i), i=0..n-1)/n;
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CROSSREFS
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Cf. A001764.
Sequence in context: A081897 A125371 A037532 this_sequence A126529 A039759 A047867
Adjacent sequences: A062233 A062234 A062235 this_sequence A062237 A062238 A062239
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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), Jun 30 2001
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