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Search: id:A120989
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| A120989 |
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Level of the first leaf (in preorder traversal) of a binary tree, summed over 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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+0
2
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| 2, 9, 34, 123, 440, 1573, 5642, 20332, 73644, 268090, 980628, 3603065, 13293540, 49234605, 182991450, 682341000, 2551955340, 9570762990, 35985909180, 135628219350, 512302356384, 1939078493154, 7353556121924, 27936898370248
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n)=Sum(k*A120988(n,k),k=1..n).
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FORMULA
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a(n)=2n(7n+13)binomial(2n+1,n)/[(n+2)(n+3)(n+4)]. G.f.=z(1+C)C^4, where C=[1-sqrt(1-4z)]/(2z) is the Catalan function. G.f.=2[1+2z-sqrt(1-4z)]/[1-2z+sqrt(1-4z)]^2.
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EXAMPLE
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a(1)=2 because for each of the trees / and \ the level of the first leaf is 1.
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MAPLE
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a:=n->2*n*(7*n+13)*binomial(2*n+1, n)/(n+2)/(n+3)/(n+4): seq(a(n), n=1..27);
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CROSSREFS
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Cf. A120988.
Sequence in context: A048498 A109719 A000524 this_sequence A010763 A077234 A091526
Adjacent sequences: A120986 A120987 A120988 this_sequence A120990 A120991 A120992
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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), Jul 30 2006
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