A342500 T(n,k) is the number of connected unlabeled posets with n elements and rank k: triangle read by rows.

1, 0, 1, 0, 2, 1, 0, 4, 5, 1, 0, 10, 24, 9, 1, 0, 27, 123, 73, 14, 1, 0, 88, 734, 638, 169, 20, 1, 0, 328, 5184, 6460, 2178, 334, 27, 1, 0, 1460, 44518, 78385, 32468, 5880, 594, 35, 1, 0, 7799, 472859, 1164966, 581533, 118933, 13605, 979, 44, 1

Offset: 1

Author

R. J. Mathar, Mar 14 2021

Keywords

• nonn
• tabl

Comments

This is a variant of A263859 admitting only connected posets.

Examples

			The table starts in row n=1 shows ranks k>=0:
1: 1
2: 0 1
3: 0 2 1
4: 0 4 5 1
5: 0 10 24 9 1
6: 0 27 123 73 14 1
7: 0 88 734 638 169 20 1
8: 0 328 5184 6460 2178 334 27 1
9: 0 1460 44518 78385 32468 5880 594 35 1
10: 0 7799 472859 1164966 581533 118933 13605 979 44 1
		

Links

• Index entries for sequences related to posets
• R. J. Mathar, Poset Illustrations

Crossrefs

Cf. A000608 (row sums), A007776 (rank 1), A263859, A000096 (subdiagonal), A342501 (labeled).

Formula

T(n,0) = 0 for k>0; due to the connectivity constraint.

T(n,n-1) = 1; the poset with elements in a single chain.