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 A320809 #5 Nov 07 2018 21:45:46
%S A320809 1,1,2,5,13,40,99,344,985,3302,10583
%N A320809 Number of non-isomorphic multiset partitions of weight n in which each part and each part of the dual, as well as the multiset union of the parts, is an aperiodic multiset.
%C A320809 Also the number of nonnegative integer matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, in which (1) the positive entries in each row and column are relatively prime and (2) the column sums are relatively prime.
%C A320809 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 A320809 A multiset is aperiodic if its multiplicities are relatively prime.
%C A320809 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 A320809 Non-isomorphic representatives of the a(1) = 1 through a(4) = 13 multiset partitions:
%e A320809 {{1}} {{1,2}} {{1,2,3}} {{1,2,3,4}}
%e A320809 {{1},{2}} {{1},{2,3}} {{1},{2,3,4}}
%e A320809 {{2},{1,2}} {{1,2},{3,4}}
%e A320809 {{1},{2},{2}} {{1,3},{2,3}}
%e A320809 {{1},{2},{3}} {{2},{1,2,2}}
%e A320809 {{3},{1,2,3}}
%e A320809 {{1},{1},{2,3}}
%e A320809 {{1},{2},{3,4}}
%e A320809 {{1},{3},{2,3}}
%e A320809 {{2},{2},{1,2}}
%e A320809 {{1},{2},{2},{2}}
%e A320809 {{1},{2},{3},{3}}
%e A320809 {{1},{2},{3},{4}}
%Y A320809 Cf. A000740, A000837, A007716, A007916, A100953, A301700, A303386, A303546, A303707, A303708, A316983, A320800-A320810, A321283.
%K A320809 nonn,more
%O A320809 0,3
%A A320809 _Gus Wiseman_, Nov 07 2018