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A327060
Number of non-isomorphic weight-n weak antichains of multisets where every two vertices appear together in some edge (cointersecting).
4
1, 1, 3, 4, 9, 11, 30, 42, 103, 194, 443
OFFSET
0,3
COMMENTS
A multiset partition is a finite multiset of finite nonempty multisets. It is a weak antichain if no part is a proper submultiset of any other.
EXAMPLE
Non-isomorphic representatives of the a(0) = 1 through a(5) = 11 multiset partitions:
{} {{1}} {{11}} {{111}} {{1111}} {{11111}}
{{12}} {{122}} {{1122}} {{11222}}
{{1}{1}} {{123}} {{1222}} {{12222}}
{{1}{1}{1}} {{1233}} {{12233}}
{{1234}} {{12333}}
{{11}{11}} {{12344}}
{{12}{12}} {{12345}}
{{12}{22}} {{11}{122}}
{{1}{1}{1}{1}} {{12}{222}}
{{33}{123}}
{{1}{1}{1}{1}{1}}
CROSSREFS
Antichains are A000372.
The BII-numbers of these set-systems are the intersection of A326853 and A326704.
Cointersecting set-systems are A327039.
The set-system version is A327057, with covering case A327058.
Sequence in context: A054075 A366753 A062798 * A270817 A182828 A294229
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 18 2019
STATUS
approved