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

1,3

Links

Table of n, a(n) for n=1..58.

Index entries for sequences related to posets

Example

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

Crossrefs

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

Sequence in context: A000171 A054922 A289651 * A302751 A350909 A244139

Adjacent sequences: A342585 A342586 A342587 * A342589 A342590 A342591

Keyword

nonn,tabf

Author

R. J. Mathar, Mar 16 2021

Status

approved