A326906 Number of sets of subsets of {1..n} that are closed under union and cover all n vertices.

2, 2, 8, 90, 4542, 2747402, 151930948472, 28175295407840207894

Offset: 0

Author

Gus Wiseman, Aug 03 2019

Keywords

• nonn
• more

Comments

Differs from A102895 in having a(0) = 2 instead of 1.

Examples

			The a(0) = 2 through a(2) = 8 sets of subsets:
  {}    {{1}}     {{1,2}}
  {{}}  {{},{1}}  {{},{1,2}}
                  {{1},{1,2}}
                  {{2},{1,2}}
                  {{},{1},{1,2}}
                  {{},{2},{1,2}}
                  {{1},{2},{1,2}}
                  {{},{1},{2},{1,2}}
		

Crossrefs

The case without empty sets is A102894.

The case with a single covering edge is A102895.

Binomial transform is A102897.

The case also closed under intersection is A326878 for n > 0.

The same for intersection instead of union is (also) A326906.

The unlabeled version is A326907.

Cf. A000798, A102896, A102897, A108800, A193675, A306445, A326880, A326881, A326883.

Programs

Mathematica

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

Formula

a(n) = 2 * A102894(n).