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A065066 Triangle T(n,k) read by rows of partially ordered sets ("posets") with n unlabeled nodes and k maximal elements (0 <= k <= n).

%I A065066 #18 Mar 14 2021 12:31:45
%S A065066 1,0,1,0,1,1,0,2,2,1,0,5,7,3,1,0,16,27,15,4,1,0,63,134,88,27,5,1,0,
%T A065066 318,814,642,221,43,6,1,0,2045,6258,5828,2319,477,64,7,1,0,16999,
%U A065066 60877,66612,30698,7015,931,90,8,1,0,183231,755323,959941,514525,133610
%N A065066 Triangle T(n,k) read by rows of partially ordered sets ("posets") with n unlabeled nodes and k maximal elements (0 <= k <= n).
%H A065066 R. J. Mathar, <a href="/A065066/b065066.txt">Table of n, a(n) for n = 0..90</a>
%H A065066 G. Brinkmann and B. D. McKay, <a href="http://users.cecs.anu.edu.au/~bdm/papers/posets.pdf">Posets on up to 16 Points</a>, Tables 8, 10, 16, 20, 24, 28, 32, 36, 40...
%H A065066 FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000068">The number of minimal elements in a poset.</a>, <a href="http://www.findstat.org/StatisticsDatabase/St000069">The number of maximal elements of a poset.</a>
%H A065066 <a href="/index/Pos#posets">Index entries for sequences related to posets</a>
%F A065066 T(n+1, 1) = Sum_{i=0}^n T(n, i) = A000112(n).
%e A065066 1,
%e A065066 0,1,
%e A065066 0,1,1,
%e A065066 0,2,2,1,
%e A065066 0,5,7,3,1,
%e A065066 0,16,27,15,4,1,
%e A065066 0,63,134,88,27,5,1,
%e A065066 0,318,814,642,221,43,6,1,
%e A065066 ...
%Y A065066 Cf. A000112.
%K A065066 nonn,tabl
%O A065066 0,8
%A A065066 _Jens Voß_, Nov 07 2001
%E A065066 Values beyond row 6 from _R. J. Mathar_, Mar 14 2021