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 A321413 #5 Nov 18 2018 15:05:49
%S A321413 1,0,0,0,0,3,0,14,13,50,65
%N A321413 Number of non-isomorphic self-dual multiset partitions of weight n with no singletons and relatively prime part sizes.
%C A321413 Also the number of nonnegative integer symmetric matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, with relatively prime row sums (or column sums) and no row (or column) summing to 1.
%C A321413 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 A321413 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 A321413 Non-isomorphic representatives of the a(5) = 3, a(7) = 14, and a(8) = 13 multiset partitions:
%e A321413 {{11}{122}} {{111}{1222}} {{111}{11222}}
%e A321413 {{11}{222}} {{111}{2222}} {{111}{22222}}
%e A321413 {{12}{122}} {{112}{1222}} {{112}{12222}}
%e A321413 {{11}{22222}} {{122}{11222}}
%e A321413 {{12}{12222}} {{11}{122}{233}}
%e A321413 {{122}{1122}} {{11}{122}{333}}
%e A321413 {{22}{11222}} {{11}{222}{333}}
%e A321413 {{11}{12}{233}} {{11}{223}{233}}
%e A321413 {{11}{22}{233}} {{12}{122}{333}}
%e A321413 {{11}{22}{333}} {{12}{123}{233}}
%e A321413 {{11}{23}{233}} {{13}{112}{233}}
%e A321413 {{12}{12}{333}} {{13}{122}{233}}
%e A321413 {{12}{13}{233}} {{23}{123}{123}}
%e A321413 {{13}{23}{123}}
%Y A321413 Cf. A000219, A007716, A120733, A138178, A302545, A316983, A319616.
%Y A321413 Cf. A320796, A320797, A320806, A320813, A321283, A321409, A321410, A321411.
%K A321413 nonn,more
%O A321413 0,6
%A A321413 _Gus Wiseman_, Nov 16 2018