A363845 Triangle read by rows: T(n,k) = number of connected n-node graphs with k nodes in distinguished bipartite block, k = 0..n.

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, 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, 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

Offset: 0

Author

Max Alekseyev, Jun 24 2023

Keywords

• nonn
• tabl

Comments

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.

Examples

			n=0: 1,
n=1: 1, 1,
n=2: 0, 1, 0,
n=3: 0, 1, 1, 0,
n=4: 0, 1, 2, 1, 0,
n=5: 0, 1, 4, 4, 1, 0,
n=6: 0, 1, 6, 13, 6, 1, 0,
n=7: 0, 1, 9, 34, 34, 9, 1, 0,
n=8: 0, 1, 12, 76, 150, 76, 12, 1, 0,
n=9: 0, 1, 16, 155, 558, 558, 155, 16, 1, 0,
...
		

Links

• Max Alekseyev, Rows n = 0..45, flattened

Crossrefs

Inverse bivariate Euler transform of A028657.

Cf. A002724, A363846.