A342589 T(n,k) is the number of posets of n labeled elements with k covering relations (n>=1, k>=0). Triangle read by rows.

1, 1, 2, 1, 6, 12, 1, 12, 60, 128, 18, 1, 20, 180, 880, 2090, 960, 100, 1, 30, 420, 3480, 17550, 47772, 43920, 15000, 1710, 140, 1, 42, 840, 10360, 84630, 452004, 1428868, 2094960, 1465170, 491540, 90594, 10080, 770

Offset: 1

Author

R. J. Mathar, Mar 16 2021

Keywords

• nonn
• tabf

Examples

			The triangle starts:
  1: 1
  2: 1 2
  3: 1 6 12
  4: 1 12 60 128 18
  5: 1 20 180 880 2090 960 100
  6: 1 30 420 3480 17550 47772 43920 15000 1710 140
  7: 1 42 840 10360 84630 452004 1428868 2094960 1465170 491540 90594 10080 770
		

Links

• Brendan McKay, Table of T(n,k) for n = 1..13
• Index entries for sequences related to posets

Crossrefs

Cf. A001035 (row sums), A002378 (k=1), A033486 (k=2?), A342447 (unlabeled), A342588 (connected).