cp's OEIS Frontend

A319784 Number of non-isomorphic intersecting T_0 set systems of weight n.

%I A319784 #6 Sep 28 2018 15:24:25
%S A319784 1,1,0,1,1,1,3,5,7,14,25
%N A319784 Number of non-isomorphic intersecting T_0 set systems of weight n.
%C A319784 A multiset partition is intersecting if no two parts are disjoint. The weight of a multiset partition is the sum of sizes of its parts. The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. The T_0 condition means the dual is strict.
%e A319784 Non-isomorphic representatives of the a(1) = 1 through a(8) = 7 multiset partitions:
%e A319784 1: {{1}}
%e A319784 3: {{2},{1,2}}
%e A319784 4: {{1,3},{2,3}}
%e A319784 5: {{3},{1,3},{2,3}}
%e A319784 6: {{3},{2,3},{1,2,3}}
%e A319784    {{1,2},{1,3},{2,3}}
%e A319784    {{1,4},{2,4},{3,4}}
%e A319784 7: {{4},{1,3,4},{2,3,4}}
%e A319784    {{1,3},{1,4},{2,3,4}}
%e A319784    {{1,3},{2,3},{1,2,3}}
%e A319784    {{1,4},{3,4},{2,3,4}}
%e A319784    {{4},{1,4},{2,4},{3,4}}
%e A319784 8: {{1,5},{2,4,5},{3,4,5}}
%e A319784    {{2,4},{3,4},{1,2,3,4}}
%e A319784    {{2,4},{1,2,5},{3,4,5}}
%e A319784    {{2,4},{1,3,4},{2,3,4}}
%e A319784    {{3},{1,3},{2,3},{1,2,3}}
%e A319784    {{4},{1,4},{3,4},{2,3,4}}
%e A319784    {{1,5},{2,5},{3,5},{4,5}}
%Y A319784 Cf. A007716, A049311, A283877, A305843, A305854, A306006, A316980, A317752.
%Y A319784 Cf. A319755, A319759, A319760, A319765, A319779, A319787, A319782, A319789.
%K A319784 nonn,more
%O A319784 0,7
%A A319784 _Gus Wiseman_, Sep 27 2018