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A036362
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Number of labeled 3-trees with n nodes.
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8
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0, 0, 1, 1, 10, 200, 5915, 229376, 10946964, 618435840, 40283203125, 2968444272640, 243926836708126, 22100985366992896, 2187905889450121295, 234881024000000000000, 27172548942138551952680, 3369317755618569294053376, 445726953911853022186520169
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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REFERENCES
| F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 30, Problem 1.13(b) with k=3.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..100
Index entries for sequences related to trees
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FORMULA
| C(n, 3)*(3*n-8)^(n-5).
Number of labeled k-trees on n nodes is binomial(n, k) * (k(n-k)+1)^(n-k-2).
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MAPLE
| [ seq(binomial(n, 3)*(3*n-8)^(n-5), n=1..20) ];
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CROSSREFS
| Cf. A000272, A036361.
Cf. A000272 (labeled trees), A036361 (labeled 2-trees), A036362 (labeled 3-trees), A036506 (labeled 4-trees), A000055 (unlabeled trees), A054581 (unlabeled 2-trees).
Sequence in context: A126431 A202436 A156275 * A051262 A178020 A041183
Adjacent sequences: A036359 A036360 A036361 * A036363 A036364 A036365
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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