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 A151880 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. 2

%I #10 May 14 2017 06:39:40

%S 1,1,1,1,1,2,3,1,3,9,12,1,4,18,52,60,1,5,30,136,360,360

%N 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.

%C All nodes are labeled except for the end-nodes.

%H F. Harary, A. Mowshowitz and J. Riordan, <a href="https://doi.org/10.1016/S0021-9800(69)80106-7">Labeled trees with unlabeled end-points</a>, J. Combin. Theory, 6 (1969), 60-64.

%F There is an explicit formula in terms of Stirling numbers of the second kind.

%e Triangle (in fact the columns in the original have been reversed and the triangle transposed):

%e (n=2) 1

%e (n=3) 1

%e (n=4) 1 1

%e (n=5) 1 2 3

%e (n=6) 1 3 9 12

%e (n=7) 1 4 18 52 60

%e (n=8) 1 5 30 136 360 360

%Y See A213262 for a better version with more terms and a program.

%Y Row sums give A001258.

%K nonn,tabf

%O 0,6

%A _N. J. A. Sloane_, Jul 21 2009

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Last modified October 2 22:30 EDT 2023. Contains 365841 sequences. (Running on oeis4.)