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A127531
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Number of jumps in all binary trees with n edges. In the preorder traversal of a binary tree, any transition from a node at a deeper level to a node on a strictly higher level is called a jump.
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1
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0, 0, 2, 13, 64, 285, 1210, 5005, 20384, 82212, 329460, 1314610, 5230016, 20764055, 82317690, 326012925, 1290244800, 5103910680, 20183646780, 79802261190, 315492902400, 1247247742650, 4930910180196, 19495286167698, 77085553829824
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n)=Sum(k*A127530(n,k), k>=0).
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REFERENCES
| W. Krandick, Trees and jumps and real roots, J. Computational and Applied Math., 162, 2004, 51-55.
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FORMULA
| a(n)=C(2n,n-2)-C(2n-2,n-2).
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MAPLE
| seq(binomial(2*n, n-2)-binomial(2*n-2, n-2), n=1..28);
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CROSSREFS
| Cf. A127530.
Sequence in context: A205532 A089130 A081340 * A037745 A037626 A160459
Adjacent sequences: A127528 A127529 A127530 * A127532 A127533 A127534
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 18 2007
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