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%I #14 Nov 27 2023 16:02:01
%S 1,0,1,5,87,6398,7745253,2414573042063,56130437190053518791691,
%T 286386577668298410118121281898931424413687
%N Number of labeled antichains of finite sets spanning n vertices without singletons.
%C From _Gus Wiseman_, Jul 03 2019: (Start)
%C Also the number of antichains covering n vertices and having empty intersection (meaning there is no vertex in common to all the edges). For example, the a(3) = 5 antichains are:
%C {{3},{1,2}}
%C {{2},{1,3}}
%C {{1},{2,3}}
%C {{1},{2},{3}}
%C {{1,2},{1,3},{2,3}}
%C (End)
%e The a(3) = 5 antichains:
%e {{1,2,3}}
%e {{1,2},{1,3}}
%e {{1,2},{2,3}}
%e {{1,3},{2,3}}
%e {{1,2},{1,3},{2,3}}
%t stableSets[u_,Q_]:=If[Length[u]==0,{{}},With[{w=First[u]},Join[stableSets[DeleteCases[u,w],Q],Prepend[#,w]&/@stableSets[DeleteCases[u,r_/;r==w||Q[r,w]||Q[w,r]],Q]]]];
%t Table[Length[Select[stableSets[Subsets[Range[n],{1,n}],SubsetQ],And[Union@@#==Range[n],#=={}||Intersection@@#=={}]&]],{n,0,5}] (* _Gus Wiseman_, Jul 03 2019 *)
%Y The binomial transform is the non-covering case A307249.
%Y The second binomial transform is A014466.
%Y Cf. A000372, A003182, A006126, A006602, A046165, A261005, A304996, A304997, A304998, A304999, A305000, A326358, A326359.
%K nonn
%O 0,4
%A _Gus Wiseman_, May 23 2018
%E a(9) from A307249 - _Dmitry I. Ignatov_, Nov 27 2023
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