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T(n,k) is the number of posets of n labeled elements with k covering relations (n>=1, k>=0). Triangle read by rows.
3

%I #8 Dec 23 2024 03:00:02

%S 1,1,2,1,6,12,1,12,60,128,18,1,20,180,880,2090,960,100,1,30,420,3480,

%T 17550,47772,43920,15000,1710,140,1,42,840,10360,84630,452004,1428868,

%U 2094960,1465170,491540,90594,10080,770

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

%H Brendan McKay, <a href="/A342589/b342589.txt">Table of T(n,k) for n = 1..13</a>

%H <a href="/index/Pos#posets">Index entries for sequences related to posets</a>

%e The triangle starts:

%e 1: 1

%e 2: 1 2

%e 3: 1 6 12

%e 4: 1 12 60 128 18

%e 5: 1 20 180 880 2090 960 100

%e 6: 1 30 420 3480 17550 47772 43920 15000 1710 140

%e 7: 1 42 840 10360 84630 452004 1428868 2094960 1465170 491540 90594 10080 770

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

%K nonn,tabf,changed

%O 1,3

%A _R. J. Mathar_, Mar 16 2021