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A326942
Number of unlabeled T_0 sets of subsets of {1..n} that cover all n vertices.
5
2, 2, 6, 58, 3770
OFFSET
0,1
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).
FORMULA
a(n) = 2 * A319637(n).
EXAMPLE
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).
Sequence in context: A137244 A284707 A174589 * A247943 A329571 A270358
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 07 2019
STATUS
approved