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%I #11 Jan 24 2020 14:40:26
%S 1,1,0,1,0,0,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,2,1,1,1,0,0,0,0,0,0,0,0,
%T 0,3,0,2,3,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,3,0,3,7,2,2,3,1,1,1,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,3,3,4,8,4,7,7,2,3,3,1,1,1
%N Triangle T(n, k) of the number of trees of order n with cutting number k >= 0.
%C The cutting number of a node v in a graph G is the number of pairs of nodes {u,w} of G such that u!=v, w!=v, and every path from u to w contains v. The cutting number of a connected graph (including trees as considered here), is the maximum cutting number of any node in the graph.
%H Sean A. Irvine, <a href="/A331238/b331238.txt">Rows n=1..27 flattened</a>
%H Frank Harary and Peter J. Slater, <a href="https://doi.org/10.1016/0020-0190(86)90093-1">A linear algorithm for the cutting center of a tree</a>, Information Processing Letters, 23 (1986), 317-319.
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a331/A331238.java">Java program</a> (github)
%H Simon Mukwembi and Senelani Dorothy Hove-Musekwa, <a href="https://doi.org/10.1007/s13226-012-0038-8">On bounds for the cutting number of a graph</a>, Indian J. Pure Appl. Math., 43 (2012), 637-649.
%e Triangle begins:
%e 1;
%e 1;
%e 0, 1;
%e 0, 0, 1, 1;
%e 0, 0, 0, 0, 1, 1, 1;
%e 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 3, 1, 1, 1;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 7, 2, 2, 3, 1, 1, 1;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 8, 4, 7, 7, 2, 3, 3, 1, 1, 1;
%e ...
%e The smallest nonzero entry on each row occurs at n-2 and the maximum at (n-1)*(n-2)/2.
%Y Cf. A000055 (row sums), A002887, A002888, A331237.
%K nonn,tabf
%O 1,23
%A _Sean A. Irvine_, Jan 16 2020
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