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%I #5 Jun 11 2018 13:13:28
%S 1,1,1,5,50,2330,1407712,229800077244,423295097236295093695
%N Number of labeled spanning intersecting antichains on n vertices.
%C An intersecting antichain S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection, and none of which is a subset of any other. S is spanning if every vertex is contained in some edge.
%H Gus Wiseman, <a href="/A048143/a048143_4.txt">Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons</a>.
%F Inverse binomial transform of A001206(n + 1).
%e The a(3) = 5 spanning intersecting 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 Length/@Table[Select[Subsets[Rest[Subsets[Range[n]]]],And[Union@@#==Range[n],FreeQ[Intersection@@@Tuples[#,2],{},{1}],Select[Tuples[#,2],UnsameQ@@#&&Complement@@#=={}&]=={}]&],{n,1,4}]
%Y Cf. A001206, A006126, A048143, A051185, A134958, A030019, A304985, A305843.
%K nonn
%O 0,4
%A _Gus Wiseman_, Jun 11 2018
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