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 A321409 #4 Nov 16 2018 07:48:59
%S A321409 1,1,1,3,6,16,27,71,135,309,621
%N A321409 Number of non-isomorphic self-dual multiset partitions of weight n whose part sizes are relatively prime.
%C A321409 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).
%C A321409 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 A321409 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 A321409 Non-isomorphic representatives of the a(1) = 1 through a(5) = 16 multiset partitions:
%e A321409 {{1}} {{1}{2}} {{1}{22}} {{1}{222}} {{11}{122}}
%e A321409 {{2}{12}} {{2}{122}} {{11}{222}}
%e A321409 {{1}{2}{3}} {{1}{1}{23}} {{12}{122}}
%e A321409 {{1}{2}{33}} {{1}{2222}}
%e A321409 {{1}{3}{23}} {{2}{1222}}
%e A321409 {{1}{2}{3}{4}} {{1}{22}{33}}
%e A321409 {{1}{23}{23}}
%e A321409 {{1}{2}{333}}
%e A321409 {{1}{3}{233}}
%e A321409 {{2}{12}{33}}
%e A321409 {{2}{13}{23}}
%e A321409 {{3}{3}{123}}
%e A321409 {{1}{2}{2}{34}}
%e A321409 {{1}{2}{3}{44}}
%e A321409 {{1}{2}{4}{34}}
%e A321409 {{1}{2}{3}{4}{5}}
%Y A321409 Cf. A000219, A007716, A120733, A138178, A316983, A319616.
%Y A321409 Cf. A320796, A320797, A320800, A320805, A320806, A320809, A320811, A320813, A321283, A321410, A321411, A321413.
%K A321409 nonn,more
%O A321409 0,4
%A A321409 _Gus Wiseman_, Nov 16 2018