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 A326946 Number of unlabeled T_0 set-systems on n vertices. 17
 1, 2, 5, 34, 1919 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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. 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 FORMULA Partial sums of A319637. a(n) = A326949(n)/2. EXAMPLE Non-isomorphic representatives of the a(0) = 1 through a(2) = 5 set-systems:   {}  {}     {}       {{1}}  {{1}}              {{1},{2}}              {{2},{1,2}}              {{1},{2},{1,2}} MATHEMATICA dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}]; Table[Length[Union[normclut/@Select[Subsets[Subsets[Range[n], {1, n}]], UnsameQ@@dual[#]&]]], {n, 0, 3}] CROSSREFS The non-T_0 version is A000612. The antichain case is A245567. The covering case is A319637. The labeled version is A326940. The version with empty edges allowed is A326949. Cf. A003180, A055621, A059052, A059201, A316978, A319559, A319564, A326942. Sequence in context: A277436 A002665 A192222 * A241586 A000665 A058882 Adjacent sequences:  A326943 A326944 A326945 * A326947 A326948 A326949 KEYWORD nonn,more AUTHOR Gus Wiseman, Aug 08 2019 STATUS approved

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Last modified February 19 19:30 EST 2020. Contains 332047 sequences. (Running on oeis4.)