cp's OEIS Frontend

A305843 Number of labeled spanning intersecting set-systems on n vertices.

%I A305843 #5 Jun 11 2018 13:13:22
%S A305843 1,1,3,27,1245,1308285,912811093455,291201248260060977862887,
%T A305843 14704022144627161780742038728709819246535634969,
%U A305843 12553242487940503914363982718112298267975272588471811456164576678961759219689708372356843289
%N A305843 Number of labeled spanning intersecting set-systems on n vertices.
%C A305843 An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. S is spanning if every vertex is contained in some edge.
%F A305843 Inverse binomial transform of A051185.
%e A305843 The a(3) = 27 spanning intersecting set-systems:
%e A305843 {{1,2,3}}
%e A305843 {{1},{1,2,3}}
%e A305843 {{2},{1,2,3}}
%e A305843 {{3},{1,2,3}}
%e A305843 {{1,2},{1,3}}
%e A305843 {{1,2},{2,3}}
%e A305843 {{1,2},{1,2,3}}
%e A305843 {{1,3},{2,3}}
%e A305843 {{1,3},{1,2,3}}
%e A305843 {{2,3},{1,2,3}}
%e A305843 {{1},{1,2},{1,3}}
%e A305843 {{1},{1,2},{1,2,3}}
%e A305843 {{1},{1,3},{1,2,3}}
%e A305843 {{2},{1,2},{2,3}}
%e A305843 {{2},{1,2},{1,2,3}}
%e A305843 {{2},{2,3},{1,2,3}}
%e A305843 {{3},{1,3},{2,3}}
%e A305843 {{3},{1,3},{1,2,3}}
%e A305843 {{3},{2,3},{1,2,3}}
%e A305843 {{1,2},{1,3},{2,3}}
%e A305843 {{1,2},{1,3},{1,2,3}}
%e A305843 {{1,2},{2,3},{1,2,3}}
%e A305843 {{1,3},{2,3},{1,2,3}}
%e A305843 {{1},{1,2},{1,3},{1,2,3}}
%e A305843 {{2},{1,2},{2,3},{1,2,3}}
%e A305843 {{3},{1,3},{2,3},{1,2,3}}
%e A305843 {{1,2},{1,3},{2,3},{1,2,3}}
%t A305843 Length/@Table[Select[Subsets[Rest[Subsets[Range[n]]]],And[Union@@#==Range[n],FreeQ[Intersection@@@Tuples[#,2],{}]]&],{n,1,4}]
%Y A305843 Cf. A001206, A006126, A048143, A051185, A134958, A030019, A304985, A305844.
%K A305843 nonn
%O A305843 0,3
%A A305843 _Gus Wiseman_, Jun 11 2018