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 A320800 #5 Nov 05 2018 21:01:23
%S A320800 1,1,1,5,14,78,157,881,2267,9257,28397
%N A320800 Number of non-isomorphic multiset partitions of weight n in which both the multiset union of the parts and the multiset union of the dual parts are aperiodic.
%C A320800 The latter condition is equivalent to the parts having relatively prime sizes.
%C A320800 A multiset is aperiodic if its multiplicities are relatively prime.
%C A320800 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 A320800 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 A320800 Non-isomorphic representatives of the a(1) = 1 through a(4) = 14 multiset partitions:
%e A320800 {{1}} {{1},{2}} {{1},{2,2}} {{1},{2,2,2}}
%e A320800 {{1},{2,3}} {{1},{2,3,3}}
%e A320800 {{2},{1,2}} {{1},{2,3,4}}
%e A320800 {{1},{2},{2}} {{2},{1,2,2}}
%e A320800 {{1},{2},{3}} {{3},{1,2,3}}
%e A320800 {{1},{1},{2,3}}
%e A320800 {{1},{2},{2,2}}
%e A320800 {{1},{2},{3,3}}
%e A320800 {{1},{2},{3,4}}
%e A320800 {{1},{3},{2,3}}
%e A320800 {{2},{2},{1,2}}
%e A320800 {{1},{2},{2},{2}}
%e A320800 {{1},{2},{3},{3}}
%e A320800 {{1},{2},{3},{4}}
%Y A320800 Cf. A000740, A000837, A007716, A007916, A100953, A301700, A303386, A303431, A303546, A303547, A316983, A320801-A320810.
%K A320800 nonn,more
%O A320800 0,4
%A A320800 _Gus Wiseman_, Nov 02 2018