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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 (list; graph; refs; listen; history; text; internal format)
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).

LINKS

Table of n, a(n) for n=0..4.

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).

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

Sequence in context: A137244 A284707 A174589 * A247943 A329571 A270358

Adjacent sequences:  A326939 A326940 A326941 * A326943 A326944 A326945

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 07 2019

STATUS

approved

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Last modified January 24 16:47 EST 2020. Contains 331209 sequences. (Running on oeis4.)