A342501 T(n,k) is the number of connected labeled posets with n elements and rank k: triangle read by rows.

1, 0, 2, 0, 6, 6, 0, 38, 84, 24, 0, 390, 1710, 840, 120, 0, 6062, 49740, 36840, 8280, 720, 0, 134526, 2050566, 2184000, 646800, 85680, 5040, 0, 4172198, 118645044, 177549624, 65313360, 10735200, 947520, 40320

Offset: 1

Author

R. J. Mathar, Mar 14 2021

Keywords

• nonn
• tabl
• hard

Comments

This is a variant of A342587 admitting only connected posets.

Examples

			The table starts in row n=1 and shows ranks k>=0:
1: 1
2: 0 2
3: 0 6 6
4: 0 38 84 24
5: 0 390 1710 840 120
6: 0 6062 49740 36840 8280 720
7: 0 134526 2050566 2184000 646800 85680 5040
8: 0 4172198 118645044 177549624 65313360 10735200 947520 40320
		

Links

• Index entries for sequences related to posets

Crossrefs

Cf. A001927 (row sums), A000142 (diagonal), A002031/A002027 (rank 1), A342500 (unlabeled).