A342588 -id:A342588 - cp's OEIS frontend

A342590 T(n,k) is the number of connected posets of n unlabeled elements with k covering relations (n>=1, k>=0). Triangle read by rows.

1, 0, 1, 0, 0, 3, 0, 0, 0, 8, 2, 0, 0, 0, 0, 27, 12, 5, 0, 0, 0, 0, 0, 91, 87, 45, 12, 3, 0, 0, 0, 0, 0, 0, 350, 532, 475, 201, 71, 14, 7, 0, 0, 0, 0, 0, 0, 0, 1376, 3272, 4298, 3197, 1565, 554, 186, 44, 16, 4, 0, 0, 0, 0, 0, 0, 0, 0, 5743, 19396, 36664, 41706, 31931, 16972

Offset: 1

R. J. Mathar, Mar 16 2021

			The table starts
1: 1
2: 0 1
3: 0 0 3
4: 0 0 0 8 2
5: 0 0 0 0 27 12   5
6: 0 0 0 0 0  91  87   45   12    3
7: 0 0 0 0 0   0 350  532  475  201   71   14   7
8: 0 0 0 0 0   0   0 1376 3272 4298 3197 1565 554 186 44 16 4

R. J. Mathar, Table of T(n,k) for n = 1..10
Index entries for sequences related to posets

Cf. A000608 (row sums), A022017 (column sums), A342447 (not necess. connected), A342588 (labeled).

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.

Original entry on oeis.org

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

R. J. Mathar, Mar 16 2021

			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

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

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

cp's OEIS Frontend

A342590 T(n,k) is the number of connected posets of n unlabeled elements with k covering relations (n>=1, k>=0). Triangle read by rows.

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