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%I #12 Dec 26 2023 13:09:09
%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 or 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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