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%I #7 Aug 19 2019 08:50:39
%S 1,1,3,4,9,11,30,42,103,194,443
%N Number of non-isomorphic weight-n weak antichains of multisets where every two vertices appear together in some edge (cointersecting).
%C 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.
%e Non-isomorphic representatives of the a(0) = 1 through a(5) = 11 multiset partitions:
%e {} {{1}} {{11}} {{111}} {{1111}} {{11111}}
%e {{12}} {{122}} {{1122}} {{11222}}
%e {{1}{1}} {{123}} {{1222}} {{12222}}
%e {{1}{1}{1}} {{1233}} {{12233}}
%e {{1234}} {{12333}}
%e {{11}{11}} {{12344}}
%e {{12}{12}} {{12345}}
%e {{12}{22}} {{11}{122}}
%e {{1}{1}{1}{1}} {{12}{222}}
%e {{33}{123}}
%e {{1}{1}{1}{1}{1}}
%Y Antichains are A000372.
%Y The BII-numbers of these set-systems are the intersection of A326853 and A326704.
%Y Cointersecting set-systems are A327039.
%Y The set-system version is A327057, with covering case A327058.
%Y Cf. A006126, A007716, A051185, A305844, A326965, A327020, A327059, A327062.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Aug 18 2019
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