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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
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.
Sequence in context: A270316 A069561 A180370 * A341303 A011148 A365307
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.)