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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.

%I A342589 #8 Dec 23 2024 03:00:02
%S A342589 1,1,2,1,6,12,1,12,60,128,18,1,20,180,880,2090,960,100,1,30,420,3480,
%T A342589 17550,47772,43920,15000,1710,140,1,42,840,10360,84630,452004,1428868,
%U A342589 2094960,1465170,491540,90594,10080,770
%N 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.
%H A342589 Brendan McKay, <a href="/A342589/b342589.txt">Table of T(n,k) for n = 1..13</a>
%H A342589 <a href="/index/Pos#posets">Index entries for sequences related to posets</a>
%e A342589 The triangle starts:
%e A342589   1: 1
%e A342589   2: 1 2
%e A342589   3: 1 6 12
%e A342589   4: 1 12 60 128 18
%e A342589   5: 1 20 180 880 2090 960 100
%e A342589   6: 1 30 420 3480 17550 47772 43920 15000 1710 140
%e A342589   7: 1 42 840 10360 84630 452004 1428868 2094960 1465170 491540 90594 10080 770
%Y A342589 Cf. A001035 (row sums), A002378 (k=1), A033486 (k=2?), A342447 (unlabeled), A342588 (connected).
%K A342589 nonn,tabf
%O A342589 1,3
%A A342589 _R. J. Mathar_, Mar 16 2021