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A326941
Number of T_0 sets of subsets of {1..n}.
14
2, 4, 14, 224, 64210, 4294322204, 18446744009291513774, 340282366920938463075992982725615419816, 115792089237316195423570985008687907843742078391854287068939455414919611614210
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 * A326940(n).
Binomial transform of A326939.
EXAMPLE
The a(0) = 2 through a(2) = 14 sets of subsets:
{} {} {}
{{}} {{}} {{}}
{{1}} {{1}}
{{},{1}} {{2}}
{{},{1}}
{{},{2}}
{{1},{2}}
{{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]]], UnsameQ@@dual[#]&]], {n, 0, 3}]
CROSSREFS
The non-T_0 version is A001146.
The covering case is A326939.
The case without empty edges is A326940.
The unlabeled version is A326949.
Sequence in context: A061291 A166105 A000370 * A132531 A123052 A064773
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 07 2019
EXTENSIONS
a(5)-a(8) from Andrew Howroyd, Aug 14 2019
STATUS
approved