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A121686
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Number of branches in all binary trees with n edges. A binary tree is a rooted tree in which each vertex has at most two children and each child of a vertex is designated as its left or right child.
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1
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2, 6, 22, 84, 324, 1254, 4862, 18876, 73372, 285532, 1112412, 4338536, 16938120, 66192390, 258909390, 1013586540, 3971224620, 15571021620, 61096813140, 239888764440, 942483155640, 3705043827420, 14573172387852, 57351122857944
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n)=Sum(k*A121685(n,k), k=1..n).
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LINKS
| Guo-Niu Han, Enumeration of Standard Puzzles
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FORMULA
| G.f.=(1-2z)[1-3z-(1-z)sqrt(1-4z)]/[z^2*sqrt(1-4z)].
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EXAMPLE
| a(1)=2 because we have two binary trees with 1 edge, namely / and \, with a total of 2 branches.
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MAPLE
| G:=(1-2*z)*(1-3*z-(1-z)*sqrt(1-4*z))/z^2/sqrt(1-4*z): Gser:=series(G, z=0, 31): seq(coeff(Gser, z, n), n=1..27);
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CROSSREFS
| Cf. A121685.
Sequence in context: A150243 A200316 A164870 * A128723 A150244 A151288
Adjacent sequences: A121683 A121684 A121685 * A121687 A121688 A121689
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 15 2006
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