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A342500 T(n,k) is the number of connected unlabeled posets with n elements and rank k: triangle read by rows.

%I A342500 #8 Mar 15 2021 14:38:51
%S A342500 1,0,1,0,2,1,0,4,5,1,0,10,24,9,1,0,27,123,73,14,1,0,88,734,638,169,20,
%T A342500 1,0,328,5184,6460,2178,334,27,1,0,1460,44518,78385,32468,5880,594,35,
%U A342500 1,0,7799,472859,1164966,581533,118933,13605,979,44,1
%N A342500 T(n,k) is the number of connected unlabeled posets with n elements and rank k: triangle read by rows.
%C A342500 This is a variant of A263859 admitting only connected posets.
%H A342500 <a href="/index/Pos#posets">Index entries for sequences related to posets</a>
%H A342500 R. J. Mathar, <a href="/A342500/a342500.pdf">Poset Illustrations</a>
%F A342500 T(n,0) = 0 for k>0; due to the connectivity constraint.
%F A342500 T(n,n-1) = 1; the poset with elements in a single chain.
%e A342500 The table starts in row n=1 shows ranks k>=0:
%e A342500 1: 1
%e A342500 2: 0 1
%e A342500 3: 0 2 1
%e A342500 4: 0 4 5 1
%e A342500 5: 0 10 24 9 1
%e A342500 6: 0 27 123 73 14 1
%e A342500 7: 0 88 734 638 169 20 1
%e A342500 8: 0 328 5184 6460 2178 334 27 1
%e A342500 9: 0 1460 44518 78385 32468 5880 594 35 1
%e A342500 10: 0 7799 472859 1164966 581533 118933 13605 979 44 1
%Y A342500 Cf. A000608 (row sums), A007776 (rank 1), A263859, A000096 (subdiagonal), A342501 (labeled).
%K A342500 nonn,tabl
%O A342500 1,5
%A A342500 _R. J. Mathar_, Mar 14 2021