

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 nonT_0 version is A000371.
The case without empty edges is A059201.
The noncovering 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 * A011148 A176020 A048650
Adjacent sequences: A326936 A326937 A326938 * A326940 A326941 A326942


KEYWORD

nonn


AUTHOR

Gus Wiseman, Aug 07 2019


STATUS

approved



