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A102893
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Number of noncrossing trees with n edges and having degree of the root at least 2.
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5
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1, 0, 1, 5, 25, 130, 700, 3876, 21945, 126500, 740025, 4382625, 26225628, 158331880, 963250600, 5899491640, 36345082425, 225082957512, 1400431689475, 8749779798375, 54874635255825, 345329274848250, 2179969531405680
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| a(n)=A001764(n) - A006013(n-1). Column 0 of A102892.
[a(n+2)]= [1,5,25,130,700,...] is the self-convolution 5-th power of A001764. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 11 2009]
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REFERENCES
| M. Noy, Enumeration of noncrossing trees on a circle, Discr. Math. 180 (1998), 301-313.
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FORMULA
| a(0)=1; a(n)=5binomial(3n-1, n-2)/(3n-1) if n>0. G.f. = g - zg^2, where g=1+zg^3 is the g.f. of the ternary numbers (A001764).
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EXAMPLE
| a(2)=1 because among the noncrossing trees with 2 edges, namely /_, _\ and /\, only the last one has root degree >1.
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MAPLE
| a:=proc(n) if n=0 then 1 else 5*binomial(3*n-1, n-2)/(3*n-1) fi end: seq(a(n), n=0..25);
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CROSSREFS
| Cf. A001764, A006013, A102892.
Sequence in context: A002002 A182626 A184139 * A094602 A144818 A048370
Adjacent sequences: A102890 A102891 A102892 * A102894 A102895 A102896
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 16 2005
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