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 A319769 #6 Sep 28 2018 15:23:13
%S A319769 1,1,2,3,5,7,12,16,26,38,61
%N A319769 Number of non-isomorphic intersecting set multipartitions (multisets of sets) of weight n whose dual is also an intersecting set multipartition.
%C A319769 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 A319769 The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%C A319769 A multiset partition is intersecting iff no two parts are disjoint. The dual of a multiset partition is intersecting iff every pair of distinct vertices appear together in some part.
%e A319769 Non-isomorphic representatives of the a(1) = 1 through a(5) = 7 set multipartitions:
%e A319769 1: {{1}}
%e A319769 2: {{1,2}}
%e A319769 {{1},{1}}
%e A319769 3: {{1,2,3}}
%e A319769 {{2},{1,2}}
%e A319769 {{1},{1},{1}}
%e A319769 4: {{1,2,3,4}}
%e A319769 {{3},{1,2,3}}
%e A319769 {{1,2},{1,2}}
%e A319769 {{2},{2},{1,2}}
%e A319769 {{1},{1},{1},{1}}
%e A319769 5: {{1,2,3,4,5}}
%e A319769 {{4},{1,2,3,4}}
%e A319769 {{2,3},{1,2,3}}
%e A319769 {{2},{1,2},{1,2}}
%e A319769 {{3},{3},{1,2,3}}
%e A319769 {{2},{2},{2},{1,2}}
%e A319769 {{1},{1},{1},{1},{1}}
%Y A319769 Cf. A007716, A281116, A283877, A305854, A306006, A316980, A316983, A317757, A319616.
%Y A319769 Cf. A319752, A319765, A319766, A319767, A319768, A319773, A319774.
%K A319769 nonn,more
%O A319769 0,3
%A A319769 _Gus Wiseman_, Sep 27 2018