%I #5 Nov 15 2018 08:40:35
%S 1,0,0,0,1,0,1,1,3,4,6
%N Number of non-isomorphic self-dual set multipartitions (multisets of sets) of weight n with no singletons.
%C Also the number of 0-1 symmetric matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, in which no row sums to 1.
%C 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 The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%e Non-isomorphic representatives of the a(4) = 1 through a(10) = 6 set multipartitions:
%e 4: {{1,2},{1,2}}
%e 6: {{1,2},{1,3},{2,3}}
%e 7: {{1,3},{2,3},{1,2,3}}
%e 8: {{2,3},{1,2,3},{1,2,3}}
%e 8: {{1,2},{1,2},{3,4},{3,4}}
%e 8: {{1,2},{1,3},{2,4},{3,4}}
%e 9: {{1,2,3},{1,2,3},{1,2,3}}
%e 9: {{1,2},{1,2},{3,4},{2,3,4}}
%e 9: {{1,2},{1,3},{1,4},{2,3,4}}
%e 9: {{1,2},{1,4},{3,4},{2,3,4}}
%e 10: {{1,2},{1,2},{1,3,4},{2,3,4}}
%e 10: {{1,2},{2,4},{1,3,4},{2,3,4}}
%e 10: {{1,3},{2,4},{1,3,4},{2,3,4}}
%e 10: {{1,4},{2,4},{3,4},{1,2,3,4}}
%e 10: {{1,2},{1,2},{3,4},{3,5},{4,5}}
%e 10: {{1,2},{1,3},{2,4},{3,5},{4,5}}
%Y Cf. A007716, A049311, A135588, A138178, A283877, A302545, A316983.
%Y Cf. A320797, A320798, A320811, A320812, A321403, A321404, A321405, A321406.
%K nonn,more
%O 0,9
%A _Gus Wiseman_, Nov 15 2018
|