A326941 Number of T_0 sets of subsets of {1..n}.

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).

Links

Table of n, a(n) for n=0..8.

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.

Cf. A003180, A059201, A316978, A319559, A319564, A319637, A326946, A326947.

Sequence in context: A061291 A166105 A000370 * A132531 A123052 A064773

Adjacent sequences: A326938 A326939 A326940 * A326942 A326943 A326944

Keyword

nonn

Author

Gus Wiseman, Aug 07 2019

Extensions

a(5)-a(8) from Andrew Howroyd, Aug 14 2019

Status

approved