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%I #7 Aug 15 2019 07:30:24
%S 1,1,2,3,6,8,17,24,51,80,180
%N Number of non-isomorphic set-systems of weight n whose dual is a weak antichain.
%C A set-system is a finite set of finite nonempty sets. The dual of a set-system has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. A weak antichain is a multiset of sets, none of which is a proper subset of any other.
%e Non-isomorphic representatives of the a(1) = 1 through a(6) = 17 multiset partitions:
%e {1} {12} {123} {1234} {12345} {123456}
%e {1}{2} {1}{23} {1}{234} {1}{2345} {1}{23456}
%e {1}{2}{3} {12}{34} {12}{345} {12}{3456}
%e {1}{2}{12} {1}{2}{345} {123}{456}
%e {1}{2}{34} {1}{23}{45} {12}{13}{23}
%e {1}{2}{3}{4} {1}{2}{3}{23} {1}{23}{123}
%e {1}{2}{3}{45} {1}{2}{3456}
%e {1}{2}{3}{4}{5} {1}{23}{456}
%e {12}{34}{56}
%e {1}{2}{13}{23}
%e {1}{2}{3}{123}
%e {1}{2}{3}{456}
%e {1}{2}{34}{56}
%e {3}{4}{12}{34}
%e {1}{2}{3}{4}{34}
%e {1}{2}{3}{4}{56}
%e {1}{2}{3}{4}{5}{6}
%Y Cf. A007716, A283877, A293993, A319643, A319721, A326966, A326968, A326970, A326972, A326973, A326974, A326975, A326978, A327017, A327019.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Aug 15 2019
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