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A067955
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Number of dissections of a convex polygon by nonintersecting diagonals into polygons with even number of sides and having a total number of n edges (sides and diagonals).
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0
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1, 0, 0, 1, 0, 1, 3, 1, 8, 13, 15, 56, 79, 157, 399, 624, 1448, 3061, 5571, 12826, 25559, 51608, 113828, 227954, 482591, 1031681, 2117323, 4542331, 9591243, 20119244, 43164172, 91165297, 193826856, 415024053, 881294603, 1886458874, 4038398755
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| Number of ordered trees with n-1 edges, all of whose nodes have odd outdegree greater than two.
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FORMULA
| a(n)=(1/n)sum(binomial(n, j)binomial((n-3-j)/2, j-1), j=1..floor((n-1)/3)) g.f. G(z) satisfies (1+z)G^3-zG^2-G+z=0
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EXAMPLE
| a(7)= 3 because the only dissections with 7 edges are given by a hexagon dissected by any of the three halving diagonals.
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MAPLE
| Order := 40: solve(series((G-G^3)/(1-G^2+G^3), G)=z, G);
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CROSSREFS
| Sequence in context: A019146 A102537 A131202 * A049965 A077108 A075847
Adjacent sequences: A067952 A067953 A067954 * A067956 A067957 A067958
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 06 2002
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