cp's OEIS Frontend

A326964 Number of connected set-systems covering a subset of {1..n}.

%I A326964 #8 Aug 12 2019 03:24:25
%S A326964 1,2,7,112,32253,2147316942,9223372023968335715,
%T A326964 170141183460469231667123699322514272668,
%U A326964 5789604461865809771178549250434395393752402807429031284280914691514037561273
%N A326964 Number of connected set-systems covering a subset of {1..n}.
%C A326964 A set-system is a finite set of finite nonempty sets.
%F A326964 Binomial transform of A323818.
%e A326964 The a(0) = 1 through a(2) = 7 set-systems:
%e A326964   {}    {}     {}
%e A326964         {{1}}  {{1}}
%e A326964                {{2}}
%e A326964                {{1,2}}
%e A326964                {{1},{1,2}}
%e A326964                {{2},{1,2}}
%e A326964                {{1},{2},{1,2}}
%t A326964 csm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[OrderedQ[#],UnsameQ@@#,Length[Intersection@@s[[#]]]>0]&]},If[c=={},s,csm[Sort[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
%t A326964 Table[Length[Select[Subsets[Subsets[Range[n],{1,n}]],Length[csm[#]]<=1&]],{n,0,4}]
%Y A326964 Covering sets of subsets are A000371.
%Y A326964 Connected graphs are A001187.
%Y A326964 The unlabeled version is A309667.
%Y A326964 The BII-numbers of connected set-systems are A326749.
%Y A326964 The covering case is A323818.
%Y A326964 Cf. A007718, A048143, A058891, A092918, A300913, A304716, A326866, A326948.
%K A326964 nonn
%O A326964 0,2
%A A326964 _Gus Wiseman_, Aug 10 2019