A342590 T(n,k) is the number of connected posets of n unlabeled elements with k covering relations (n>=1, k>=0). Triangle read by rows.

1, 0, 1, 0, 0, 3, 0, 0, 0, 8, 2, 0, 0, 0, 0, 27, 12, 5, 0, 0, 0, 0, 0, 91, 87, 45, 12, 3, 0, 0, 0, 0, 0, 0, 350, 532, 475, 201, 71, 14, 7, 0, 0, 0, 0, 0, 0, 0, 1376, 3272, 4298, 3197, 1565, 554, 186, 44, 16, 4, 0, 0, 0, 0, 0, 0, 0, 0, 5743, 19396, 36664, 41706, 31931, 16972

Offset: 1

Author

R. J. Mathar, Mar 16 2021

Keywords

• nonn
• tabf

Examples

			The table starts
1: 1
2: 0 1
3: 0 0 3
4: 0 0 0 8 2
5: 0 0 0 0 27 12   5
6: 0 0 0 0 0  91  87   45   12    3
7: 0 0 0 0 0   0 350  532  475  201   71   14   7
8: 0 0 0 0 0   0   0 1376 3272 4298 3197 1565 554 186 44 16 4
		

Links

• R. J. Mathar, Table of T(n,k) for n = 1..10
• Index entries for sequences related to posets

Crossrefs

Cf. A000608 (row sums), A022017 (column sums), A342447 (not necess. connected), A342588 (labeled).