[seqfan] more poset enumerations

[Richard J. Mathar]

We now have A342500 and A342501 (posets by maximum chain length),
and apparently useful would also be the following 3 triangles (all values need TBC):

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The number of labeled connected posets enumerated by number of arcs
(row sums A001927):

1: 1 (1)
2: 0 2 (2)
3: 0 0 12 (12)
4: 0 0 0 128 18 (146)
5: 0 0 0 0 2000 960 100 (3060)
6: 0 0 0 0 0 41472 43320 15000 1710 140 (101642)
7: 0 0 0 0 0 0 1075648 1985760 1453200 490560 90594 10080 770 (5106612)

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The number of labeled posets enumerated by number of arcs:
(row sums A001035, unlabeled are A342447):

1: 1 (1)
2: 1 2 (3)
3: 1 6 12 (19)
4: 1 12 60 128 18 (219)
5: 1 20 180 880 2090 960 100 (4231)
6: 1 30 420 3480 17550 47772 43920 15000 1710 140 (130023)
7: 1 42 840 10360 84630 452004 1428868 2094960 1465170 491540 90594 10080 770 (6129859)

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The number of connected unlabeled posets enumerated by number of arcs:
(row sums A000608):
1: 1 (1)
2: 0 1 (1)
3: 0 0 3 (3)
4: 0 0 0 8 2 (10)
5: 0 0 0 0 27 12 5 (44)
6: 0 0 0 0 0 91 87 45 12 3 (238)
7: 0 0 0 0 0 0 350 532 475 201 71 14 7 (1650)