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%I #11 Nov 03 2019 15:54:54
%S 1,1,1,1,1,1,1,1,1,2,2,1,1,2,4,2,1,1,3,7,7,3,1,1,3,10,14,10,3,1,1,4,
%T 14,28,28,14,4,1,1,4,19,45,65,45,19,4,1,1,5,24,73,132,132,73,24,5,1,1,
%U 5,30,105,242,316,242,105,30,5,1,1,6,37,152,412,693,693,412,152
%N Triangle read by rows: T(n,k) = number of unlabeled free bicolored trees with n nodes (n >= 1) and k (1 <= k <= n-1, except k=0 or 1 if n=1, k=1 if n=2) nodes of one color and n-k nodes of the other color (the colors are not interchangeable).
%D R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.
%H R. W. Robinson, <a href="/A122085/b122085.txt">Rows 1 through 30, flattened</a>
%e K M N gives the number N of unlabeled free bicolored trees with K nodes of one color and M nodes of the other color.
%e 0 1 1
%e 1 0 1
%e Total( 1) = 2
%e 1 1 1
%e Total( 2) = 1
%e 1 2 1
%e 2 1 1
%e Total( 3) = 2
%e 1 3 1
%e 2 2 1
%e 3 1 1
%e Total( 4) = 3
%e 1 4 1
%e 2 3 2
%e 3 2 2
%e 4 1 1
%e Total( 5) = 6
%e 1 5 1
%e 2 4 2
%e 3 3 4
%e 4 2 2
%e 5 1 1
%e Total( 6) = 10
%e .
%e From _Andrew Howroyd_, Nov 02 2019: (Start)
%e Triangle for n >= 2, 1 <= k < n:
%e 2 | 1;
%e 3 | 1, 1;
%e 4 | 1, 1, 1;
%e 5 | 1, 2, 2, 1;
%e 6 | 1, 2, 4, 2, 1;
%e 7 | 1, 3, 7, 7, 3, 1;
%e 8 | 1, 3, 10, 14, 10, 3, 1;
%e 9 | 1, 4, 14, 28, 28, 14, 4, 1;
%e 10 | 1, 4, 19, 45, 65, 45, 19, 4, 1;
%e 11 | 1, 5, 24, 73, 132, 132, 73, 24, 5, 1;
%e 12 | 1, 5, 30, 105, 242, 316, 242, 105, 30, 5, 1;
%e ...
%e (End)
%Y Row sums give A122086.
%Y Cf. A329054 (regular array with same data).
%K nonn,tabf
%O 1,10
%A _N. J. A. Sloane_, Oct 19 2006
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