A342588 T(n,k) is the number of labeled connected posets of n labeled elements with k covering relations (n>=1, k>=0). Triangle read by rows.

1, 0, 2, 0, 0, 12, 0, 0, 0, 128, 18, 0, 0, 0, 0, 2000, 960, 100, 0, 0, 0, 0, 0, 41472, 43320, 15000, 1710, 140, 0, 0, 0, 0, 0, 0, 1075648, 1985760, 1453200, 490560, 90594, 10080, 770, 0, 0, 0, 0, 0, 0, 0, 33554432, 96937680, 122360000, 82220880, 32527488, 8205288, 1396640, 179760, 20048, 1050

Offset: 1

Author

R. J. Mathar, Mar 16 2021

Keywords

• nonn
• tabf

Examples

			There are 8 connected unlabeled Hasse diagrams on 4 nodes with 3 arcs. 4 of them have automorphism group order 1, 2 of them have automorphism group order 2 and 2 have order 6. So T(4,3) = 4*4!/1 + 2*4!/2 + 2*4!/6 = 128.
There are 2 connected unlabeled Hasse diagrams on 4 nodes with 4 arcs, one has automorphism group order 2, the other 4. So T(4,4) = 1*4!/2+1*4!/4 = 18.
The triangle starts
1: 1
2: 0 2
3: 0 0 12
4: 0 0  0 128   18
5: 0 0  0   0 2000   960     100
6: 0 0  0   0    0 41472   43320   15000    1710    140
7: 0 0  0   0    0     0 1075648 1985760 1453200 490560 90594 10080 770
		

Links

• Index entries for sequences related to posets

Crossrefs

Cf. A001927 (row sums), A342589 (not necessarily connected), A342590 (unlabeled).