A326942 Number of unlabeled T_0 sets of subsets of {1..n} that cover all n vertices.

2, 2, 6, 58, 3770

Offset: 0

Author

Gus Wiseman, Aug 07 2019

Keywords

• nonn
• more

Comments

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. The T_0 condition means that the dual is strict (no repeated edges).

Examples

			Non-isomorphic representatives of the a(0) = 2 through a(2) = 6 sets of subsets:
  {}    {{1}}     {{1},{2}}
  {{}}  {{},{1}}  {{2},{1,2}}
                  {{},{1},{2}}
                  {{},{2},{1,2}}
                  {{1},{2},{1,2}}
                  {{},{1},{2},{1,2}}
		

Crossrefs

The non-T_0 version is A003181.

The case without empty edges is A319637.

The labeled version is A326939.

The non-covering version is A326949 (partial sums).

Cf. A000371, A003180, A055621, A059201, A316978, A319559, A319564, A326907, A326941, A326943, A326946.

Formula

a(n) = 2 * A319637(n).