%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 n1 (to 2 if n = 2), where R*(n,k) = number of trees with n nodes and k unlabeled endnodes.
%C All nodes are labeled except for the endnodes.
%H F. Harary, A. Mowshowitz and J. Riordan, <a href="https://doi.org/10.1016/S00219800(69)801067">Labeled trees with unlabeled endpoints</a>, J. Combin. Theory, 6 (1969), 6064.
%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
