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A297877 Triangle T(n,k) read by rows, giving number of bipartite graphs with n nodes (n >= 0) and k edges (0 <= k <= floor(n/2*n/2)).

%I A297877 #20 Feb 28 2018 04:59:36
%S A297877 1,1,1,1,1,1,1,1,1,2,2,1,1,1,2,3,4,1,1,1,1,2,4,7,8,6,3,2,1,1,1,2,4,8,
%T A297877 13,19,14,13,7,4,1,1,1,1,2,4,9,16,32,45,52,48,40,24,16,7,3,2,1,1,1,2,
%U A297877 4,9,17,38,70,120,150,179,164,143,94,63,32,19,7,4,1,1,1,1,2,4,9,18,41,85,181,324,500,659
%N A297877 Triangle T(n,k) read by rows, giving number of bipartite graphs with n nodes (n >= 0) and k edges (0 <= k <= floor(n/2*n/2)).
%C A297877 The sum of the m-th row is the (m-1)-st member of A033995, number of bipartite graphs with n nodes.
%D A297877 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, New York / London, 1973.
%H A297877 P. Hanlon, <a href="http://dx.doi.org/10.1016/0012-365X(79)90184-5">The enumeration of bipartite graphs</a>, Discrete Math. 28 (1979), 49-57.
%H A297877 Juergen Will, <a href="/A297877/a297877.txt">Rows 0 to 10 of triangle.</a>
%e A297877 Triangle begins:
%e A297877 0:  1;
%e A297877 1:  1;
%e A297877 2:  1,  1;
%e A297877 3:  1,  1,  1;
%e A297877 4:  1,  1,  2,  2,  1;
%e A297877 5:  1,  1,  2,  3,  4,  1,  1;
%e A297877 6:  1,  1,  2,  4,  7,  8,  6,  3,  2,  1;
%e A297877 7:  1,  1,  2,  4,  8, 13, 19, 14, 13,  7,  4,  1,  1;
%Y A297877 Cf. A033995 (row sums).
%K A297877 nonn,tabf
%O A297877 0,10
%A A297877 _Juergen Will_, Jan 07 2018