cp's OEIS Frontend

A319779 Number of intersecting multiset partitions of weight n whose dual is not an intersecting multiset partition.

%I A319779 #5 Sep 28 2018 15:23:57
%S A319779 1,0,0,0,1,4,20,66,226,696,2156
%N A319779 Number of intersecting multiset partitions of weight n whose dual is not an intersecting multiset partition.
%C A319779 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}}.
%C A319779 The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%C A319779 A multiset partition is intersecting iff no two parts are disjoint. The dual of a multiset partition is intersecting iff every pair of distinct vertices appear together in some part.
%e A319779 Non-isomorphic representatives of the a(4) = 1 through a(6) = 20 multiset partitions:
%e A319779 4: {{1,3},{2,3}}
%e A319779 5: {{1,2},{2,3,3}}
%e A319779    {{1,3},{2,3,3}}
%e A319779    {{1,4},{2,3,4}}
%e A319779    {{3},{1,3},{2,3}}
%e A319779 6: {{1,2},{2,3,3,3}}
%e A319779    {{1,3},{2,2,3,3}}
%e A319779    {{1,3},{2,3,3,3}}
%e A319779    {{1,3},{2,3,4,4}}
%e A319779    {{1,4},{2,3,4,4}}
%e A319779    {{1,5},{2,3,4,5}}
%e A319779    {{1,1,2},{2,3,3}}
%e A319779    {{1,2,2},{2,3,3}}
%e A319779    {{1,2,3},{3,4,4}}
%e A319779    {{1,2,4},{3,4,4}}
%e A319779    {{1,2,5},{3,4,5}}
%e A319779    {{1,3,3},{2,3,3}}
%e A319779    {{1,3,4},{2,3,4}}
%e A319779    {{2},{1,2},{2,3,3}}
%e A319779    {{3},{1,3},{2,3,3}}
%e A319779    {{4},{1,4},{2,3,4}}
%e A319779    {{1,3},{2,3},{2,3}}
%e A319779    {{1,3},{2,3},{3,3}}
%e A319779    {{1,4},{2,4},{3,4}}
%e A319779    {{3},{3},{1,3},{2,3}}
%Y A319779 Cf. A007716, A281116, A283877, A305854, A306006, A316980, A316983, A317757, A319616.
%Y A319779 Cf. A319775, A319778, A319781, A319783.
%K A319779 nonn,more
%O A319779 0,6
%A A319779 _Gus Wiseman_, Sep 27 2018