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 A326939 Number of T_0 sets of subsets of {1..n} that cover all n vertices. 15
 2, 2, 8, 192, 63384, 4294003272, 18446743983526539408, 340282366920938462946865774750753349904, 115792089237316195423570985008687907841019819456486779364848020385134373080448 (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..8. FORMULA a(n) = 2 * A059201(n). Inverse binomial transform of A326941. EXAMPLE The a(0) = 2 through a(2) = 8 sets of subsets: {} {{1}} {{1},{2}} {{}} {{},{1}} {{1},{1,2}} {{2},{1,2}} {{},{1},{2}} {{},{1},{1,2}} {{},{2},{1,2}} {{1},{2},{1,2}} {{},{1},{2},{1,2}} MATHEMATICA dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}]; Table[Length[Select[Subsets[Subsets[Range[n]]], Union@@#==Range[n]&&UnsameQ@@dual[#]&]], {n, 0, 3}] CROSSREFS The non-T_0 version is A000371. The case without empty edges is A059201. The non-covering version is A326941. The unlabeled version is A326942. The case closed under intersection is A326943. Cf. A003180, A003181, A003465, A316978, A319564, A319637, A326940, A326947. Sequence in context: A270316 A069561 A180370 * A341303 A011148 A365307 Adjacent sequences: A326936 A326937 A326938 * A326940 A326941 A326942 KEYWORD nonn AUTHOR Gus Wiseman, Aug 07 2019 STATUS approved

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Last modified April 23 07:11 EDT 2024. Contains 371905 sequences. (Running on oeis4.)