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

1,3

Comments

This is a variant of A342587 admitting only connected posets.

Links

Table of n, a(n) for n=1..36.

Index entries for sequences related to posets

Example

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

Crossrefs

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

Sequence in context: A142354 A105110 A351884 * A064696 A021488 A296040

Adjacent sequences: A342498 A342499 A342500 * A342502 A342503 A342504

Keyword

nonn,tabl,hard

Author

R. J. Mathar, Mar 14 2021

Status

approved