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Triangle read by rows: T(n,k) = number of connected n-node graphs with k nodes in distinguished bipartite block, k = 0..n.
3

%I #14 Jun 24 2023 16:02:40

%S 1,1,1,0,1,0,0,1,1,0,0,1,2,1,0,0,1,4,4,1,0,0,1,6,13,6,1,0,0,1,9,34,34,

%T 9,1,0,0,1,12,76,150,76,12,1,0,0,1,16,155,558,558,155,16,1,0,0,1,20,

%U 290,1824,3529,1824,290,20,1,0,0,1,25,510,5375,19687,19687,5375,510,25,1,0,0,1,30,853,14549,98726,194203,98726,14549,853,30,1,0

%N Triangle read by rows: T(n,k) = number of connected n-node graphs with k nodes in distinguished bipartite block, k = 0..n.

%C Also, rectangular array read by antidiagonals: A(m,n) = number of distinct m X n binary matrices M up to permutations of rows or columns such that M represents the reduced adjacency matrix of a connected bipartite graph.

%H Max Alekseyev, <a href="/A363845/b363845.txt">Rows n = 0..45, flattened</a>

%e n=0: 1,

%e n=1: 1, 1,

%e n=2: 0, 1, 0,

%e n=3: 0, 1, 1, 0,

%e n=4: 0, 1, 2, 1, 0,

%e n=5: 0, 1, 4, 4, 1, 0,

%e n=6: 0, 1, 6, 13, 6, 1, 0,

%e n=7: 0, 1, 9, 34, 34, 9, 1, 0,

%e n=8: 0, 1, 12, 76, 150, 76, 12, 1, 0,

%e n=9: 0, 1, 16, 155, 558, 558, 155, 16, 1, 0,

%e ...

%Y Inverse bivariate Euler transform of A028657.

%Y Cf. A002724, A363846.

%K nonn,tabl

%O 0,13

%A _Max Alekseyev_, Jun 24 2023