A326881 Number of set-systems with {} that are closed under intersection and cover n vertices.

1, 1, 5, 71, 4223, 2725521, 151914530499, 28175294344381108057

Offset: 0

Author

Gus Wiseman, Jul 30 2019

Keywords

• nonn
• more

Examples

			The a(2) = 5 set-systems:
  {{},{1,2}}
  {{},{1},{2}}
  {{},{1},{1,2}}
  {{},{2},{1,2}}
  {{},{1},{2},{1,2}}
		

Crossrefs

The case also closed under union is A000798.

The connected case (i.e., with maximum) is A102894.

The same for union instead of intersection is (also) A102894.

The non-covering case is A102895.

The BII-numbers of these set-systems (without the empty set) are A326880.

The unlabeled case is A326883.

Cf. A003465, A014466, A102896, A102897, A193674, A193675, A306445, A307249, A326878.

Programs

Mathematica

Table[Length[Select[Subsets[Subsets[Range[n]]],MemberQ[#,{}]&&Union@@#==Range[n]&&SubsetQ[#,Intersection@@@Tuples[#,2]]&]],{n,0,3}]

Formula

Inverse binomial transform of A102895. - Andrew Howroyd, Aug 10 2019

Extensions

a(5)-a(7) from Andrew Howroyd, Aug 10 2019