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 A322111 #4 Nov 27 2018 16:18:05
%S A322111 1,1,1,2,2,5,5,13,13,37,37
%N A322111 Number of non-isomorphic self-dual connected multiset partitions of weight n with multiset density -1.
%C A322111 The multiset density of a multiset partition is the sum of the numbers of distinct vertices in each part minus the number of parts minus the number of vertices.
%C A322111 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}}. A multiset partition is self-dual if it is isomorphic to its dual. For example, {{1,1},{1,2,2},{2,3,3}} is self-dual, as it is isomorphic to its dual {{1,1,2},{2,2,3},{3,3}}.
%C A322111 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 A322111 Non-isomorphic representatives of the a(1) = 1 through a(8) = 13 multiset partitions:
%e A322111 {{1}} {{1,1}}
%e A322111 .
%e A322111 {{1,1,1}} {{1,1,1,1}}
%e A322111 {{2},{1,2}} {{2},{1,2,2}}
%e A322111 .
%e A322111 {{1,1,1,1,1}} {{1,1,1,1,1,1}}
%e A322111 {{1,1},{1,2,2}} {{2},{1,2,2,2,2}}
%e A322111 {{2},{1,2,2,2}} {{2,2},{1,1,2,2}}
%e A322111 {{2},{1,3},{2,3}} {{2},{1,3},{2,3,3}}
%e A322111 {{3},{3},{1,2,3}} {{3},{3},{1,2,3,3}}
%e A322111 .
%e A322111 {{1,1,1,1,1,1,1}} {{1,1,1,1,1,1,1,1}}
%e A322111 {{1,1,1},{1,2,2,2}} {{1,1,1},{1,1,2,2,2}}
%e A322111 {{2},{1,2,2,2,2,2}} {{2},{1,2,2,2,2,2,2}}
%e A322111 {{2,2},{1,1,2,2,2}} {{2,2},{1,1,2,2,2,2}}
%e A322111 {{1,1},{1,2},{2,3,3}} {{1,1},{1,2,2},{2,3,3}}
%e A322111 {{2},{1,3},{2,3,3,3}} {{2},{1,3},{2,3,3,3,3}}
%e A322111 {{2},{2,2},{1,2,3,3}} {{2},{1,3,3},{2,2,3,3}}
%e A322111 {{3},{1,2,2},{2,3,3}} {{3},{3},{1,2,3,3,3,3}}
%e A322111 {{3},{3},{1,2,3,3,3}} {{3},{3,3},{1,2,2,3,3}}
%e A322111 {{1},{1},{1,4},{2,3,4}} {{2},{1,3},{2,4},{3,4,4}}
%e A322111 {{2},{1,3},{2,4},{3,4}} {{3},{3},{1,2,4},{3,4,4}}
%e A322111 {{3},{4},{1,4},{2,3,4}} {{3},{4},{1,4},{2,3,4,4}}
%e A322111 {{4},{4},{4},{1,2,3,4}} {{4},{4},{4},{1,2,3,4,4}}
%Y A322111 Cf. A000272, A007716, A007718, A030019, A052888, A134954, A304867, A304887, A316983, A318697, A319616, A321155, A321255.
%K A322111 nonn,more
%O A322111 0,4
%A A322111 _Gus Wiseman_, Nov 26 2018