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A151880
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Triangle: R*(n,k) (n>=2, k from 2 to n-1 (to 2 if n = 2), where R*(n,k) = number of trees with n nodes and k unlabeled end-nodes.
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1
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1, 1, 1, 1, 1, 2, 3, 1, 3, 9, 12, 1, 4, 18, 52, 60, 1, 5, 30, 136, 360, 360
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| All nodes are labeled except for some of the end-nodes.
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REFERENCES
| F. Harary, A. Mowshowitz and J. Riordan, Labeled trees with unlabeled end-points, J. Combin. Theory, 6 (1969), 60-64.
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FORMULA
| There is an explicit formula in terms of Stirling numbers of the second kind.
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EXAMPLE
| Triangle (in fact the columns in the original have been reversed and the triangle transposed):
(n=2) 1
(n=3) 1
(n=4) 1 1
(n=5) 1 2 3
(n=6) 1 3 9 12
(n=7) 1 4 18 52 60
(n=8) 1 5 30 136 360 360
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CROSSREFS
| Row sums give A001258.
Sequence in context: A171150 A111589 A010027 * A108990 A145080 A065078
Adjacent sequences: A151877 A151878 A151879 * A151881 A151882 A151883
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KEYWORD
| nonn,tabf
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jul 21 2009
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