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%I #9 Mar 16 2021 08:30:49
%S 1,0,2,0,6,6,0,38,84,24,0,390,1710,840,120,0,6062,49740,36840,8280,
%T 720,0,134526,2050566,2184000,646800,85680,5040,0,4172198,118645044,
%U 177549624,65313360,10735200,947520,40320
%N T(n,k) is the number of connected labeled posets with n elements and rank k: triangle read by rows.
%C This is a variant of A342587 admitting only connected posets.
%H <a href="/index/Pos#posets">Index entries for sequences related to posets</a>
%e The table starts in row n=1 and shows ranks k>=0:
%e 1: 1
%e 2: 0 2
%e 3: 0 6 6
%e 4: 0 38 84 24
%e 5: 0 390 1710 840 120
%e 6: 0 6062 49740 36840 8280 720
%e 7: 0 134526 2050566 2184000 646800 85680 5040
%e 8: 0 4172198 118645044 177549624 65313360 10735200 947520 40320
%Y Cf. A001927 (row sums), A000142 (diagonal), A002031/A002027 (rank 1), A342500 (unlabeled).
%K nonn,tabl,hard
%O 1,3
%A _R. J. Mathar_, Mar 14 2021
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