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A342588 T(n,k) is the number of labeled connected posets of n labeled elements with k covering relations (n>=1, k>=0). Triangle read by rows.

%I A342588 #10 Mar 16 2021 18:29:11
%S A342588 1,0,2,0,0,12,0,0,0,128,18,0,0,0,0,2000,960,100,0,0,0,0,0,41472,43320,
%T A342588 15000,1710,140,0,0,0,0,0,0,1075648,1985760,1453200,490560,90594,
%U A342588 10080,770,0,0,0,0,0,0,0,33554432,96937680,122360000,82220880,32527488,8205288,1396640,179760,20048,1050
%N A342588 T(n,k) is the number of labeled connected posets of n labeled elements with k covering relations (n>=1, k>=0). Triangle read by rows.
%H A342588 <a href="/index/Pos#posets">Index entries for sequences related to posets</a>
%e A342588 There are 8 connected unlabeled Hasse diagrams on 4 nodes with 3 arcs. 4 of them have automorphism group order 1, 2 of them have automorphism group order 2 and 2 have order 6. So T(4,3) = 4*4!/1 + 2*4!/2 + 2*4!/6 = 128.
%e A342588 There are 2 connected unlabeled Hasse diagrams on 4 nodes with 4 arcs, one has automorphism group order 2, the other 4. So T(4,4) = 1*4!/2+1*4!/4 = 18.
%e A342588 The triangle starts
%e A342588 1: 1
%e A342588 2: 0 2
%e A342588 3: 0 0 12
%e A342588 4: 0 0  0 128   18
%e A342588 5: 0 0  0   0 2000   960     100
%e A342588 6: 0 0  0   0    0 41472   43320   15000    1710    140
%e A342588 7: 0 0  0   0    0     0 1075648 1985760 1453200 490560 90594 10080 770
%Y A342588 Cf. A001927 (row sums), A342589 (not necessarily connected), A342590 (unlabeled).
%K A342588 nonn,tabf
%O A342588 1,3
%A A342588 _R. J. Mathar_, Mar 16 2021