This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A321404 #5 Nov 15 2018 08:40:35
%S A321404 1,0,0,0,1,0,1,1,3,4,6
%N A321404 Number of non-isomorphic self-dual set multipartitions (multisets of sets) of weight n with no singletons.
%C A321404 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 A321404 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 A321404 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 A321404 Non-isomorphic representatives of the a(4) = 1 through a(10) = 6 set multipartitions:
%e A321404 4: {{1,2},{1,2}}
%e A321404 6: {{1,2},{1,3},{2,3}}
%e A321404 7: {{1,3},{2,3},{1,2,3}}
%e A321404 8: {{2,3},{1,2,3},{1,2,3}}
%e A321404 8: {{1,2},{1,2},{3,4},{3,4}}
%e A321404 8: {{1,2},{1,3},{2,4},{3,4}}
%e A321404 9: {{1,2,3},{1,2,3},{1,2,3}}
%e A321404 9: {{1,2},{1,2},{3,4},{2,3,4}}
%e A321404 9: {{1,2},{1,3},{1,4},{2,3,4}}
%e A321404 9: {{1,2},{1,4},{3,4},{2,3,4}}
%e A321404 10: {{1,2},{1,2},{1,3,4},{2,3,4}}
%e A321404 10: {{1,2},{2,4},{1,3,4},{2,3,4}}
%e A321404 10: {{1,3},{2,4},{1,3,4},{2,3,4}}
%e A321404 10: {{1,4},{2,4},{3,4},{1,2,3,4}}
%e A321404 10: {{1,2},{1,2},{3,4},{3,5},{4,5}}
%e A321404 10: {{1,2},{1,3},{2,4},{3,5},{4,5}}
%Y A321404 Cf. A007716, A049311, A135588, A138178, A283877, A302545, A316983.
%Y A321404 Cf. A320797, A320798, A320811, A320812, A321403, A321404, A321405, A321406.
%K A321404 nonn,more
%O A321404 0,9
%A A321404 _Gus Wiseman_, Nov 15 2018