OFFSET
0,2
COMMENTS
A set-system is a finite set of finite nonempty sets, so no two edges of such a set-system can be disjoint.
EXAMPLE
The a(0) = 1 through a(3) = 29 set-systems:
{} {} {} {}
{{1}} {{1}} {{1}}
{{2}} {{2}}
{{1,2}} {{3}}
{{1},{1,2}} {{1,2}}
{{2},{1,2}} {{1,3}}
{{2,3}}
{{1,2,3}}
{{1},{1,2}}
{{1},{1,3}}
{{2},{1,2}}
{{2},{2,3}}
{{3},{1,3}}
{{3},{2,3}}
{{1},{1,2,3}}
{{2},{1,2,3}}
{{3},{1,2,3}}
{{1,2},{1,2,3}}
{{1,3},{1,2,3}}
{{2,3},{1,2,3}}
{{1},{1,2},{1,2,3}}
{{1},{1,3},{1,2,3}}
{{2},{1,2},{1,2,3}}
{{2},{2,3},{1,2,3}}
{{3},{1,3},{1,2,3}}
{{3},{2,3},{1,2,3}}
{{1},{1,2},{1,3},{1,2,3}}
{{2},{1,2},{2,3},{1,2,3}}
{{3},{1,3},{2,3},{1,2,3}}
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], SubsetQ[#, Union[Union@@@Tuples[#, 2], Intersection@@@Tuples[#, 2]]]&]], {n, 0, 3}]
(* Second program: *)
a[n_] := Sum[Binomial[n, k] A006058[[k + 1]], {k, 0, n}];
a /@ Range[0, 18] (* Jean-François Alcover, Jan 01 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 04 2019
EXTENSIONS
a(16)-a(18) from A006058 by Jean-François Alcover, Jan 01 2020
STATUS
approved