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A151880 Triangle: R*(n,k) (n>=2, k from 2 to n-1 or to 2 if n = 2), where R*(n,k) = number of trees with n nodes and k unlabeled end-nodes. 2
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; text; internal format)
OFFSET
0,6
COMMENTS
All nodes are labeled except for the end-nodes.
LINKS
F. Harary, A. Mowshowitz and J. Riordan, Labeled trees with unlabeled end-points, J. Combin. Theory, 6 (1969), 60-64.
FORMULA
There is an explicit formula in terms of Stirling numbers of the second kind.
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
CROSSREFS
See A213262 for a better version with more terms and a program.
Row sums give A001258.
Sequence in context: A111589 A259760 A010027 * A108990 A145080 A065078
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jul 21 2009
STATUS
approved

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Last modified July 25 11:18 EDT 2024. Contains 374588 sequences. (Running on oeis4.)