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A317674 Regular triangle where T(n,k) is the number of antichains covering n vertices with k connected components.

%I A317674 #5 Aug 04 2018 06:41:36
%S A317674 1,1,1,5,3,1,84,23,6,1,6348,470,65,10,1,7743728,39598,1575,145,15,1,
%T A317674 2414572893530,54354104,144403,4095,280,21,1,56130437190053299918162,
%U A317674 19316801997024,218033088,402073,9100,490,28,1
%N A317674 Regular triangle where T(n,k) is the number of antichains covering n vertices with k connected components.
%H A317674 Gus Wiseman, <a href="/A048143/a048143_4.txt">Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons</a>.
%e A317674 Triangle begins:
%e A317674         1
%e A317674         1       1
%e A317674         5       3       1
%e A317674        84      23       6       1
%e A317674      6348     470      65      10       1
%e A317674   7743728   39598    1575     145      15       1
%t A317674 blg={1,1,5,84,6348,7743728,2414572893530,56130437190053299918162} (*A048143*);
%t A317674 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A317674 Table[Sum[Product[blg[[Length[s]]],{s,spn}],{spn,Select[sps[Range[n]],Length[#]==k&]}],{n,Length[blg]},{k,n}]
%Y A317674 First column is A048143. Row sums are A006126.
%Y A317674 Cf. A000272, A001187, A013922, A030019, A134954, A143543, A275307, A293510.
%Y A317674 Cf. A317634, A317635, A317671, A317672, A317677.
%K A317674 nonn,tabl
%O A317674 1,4
%A A317674 _Gus Wiseman_, Aug 03 2018