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A052526
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Number of labeled rooted trees with n leaves in which the degrees of the root and all internal nodes are >= 3.
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1
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0, 0, 0, 1, 1, 11, 36, 372, 2311, 26252, 243893, 3173281, 38916879, 583922418, 8808814262, 151530476047, 2694658394356, 52607648010035, 1072975736368359, 23516009286474813, 539838208864165036
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| Old name was "Non-planar labeled trees with neither unary nor binary nodes". "Non-planar" presumably indicates that we are only concerned with the abstract tree, not with a particular embedding in the plane.
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 96
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FORMULA
| E.g.f.: RootOf(2*exp(Z)-4*Z+2*x-2-Z^2)-x
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EXAMPLE
| For n=5 there are 2 unlabeled trees of this type. In the first, the root node has 5 children which are all leaves. In the second, the root has 3 children; 2 are leaves and 1 has 3 children which are leaves. The first has only one labeling; the second has binomial(5,2)=10 labelings. So a(5) = 1 + 10 = 11.
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MAPLE
| Non spec := [S, {B=Union(S, Z), S=Set(B, 3 <= card)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
| Unlabeled trees of this type are counted by A052525. Labeled trees in which the degrees of non-leaf nodes are >= 2 are counted by A000311.
Sequence in context: A006505 A004637 A191296 * A195201 A054293 A072859
Adjacent sequences: A052523 A052524 A052525 * A052527 A052528 A052529
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jun 07 2006
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