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 A319782 #5 Sep 28 2018 15:24:11
%S A319782 1,1,1,4,7,17,42,98,248,631,1657
%N A319782 Number of non-isomorphic intersecting strict T_0 multiset partitions of weight n.
%C A319782 A multiset partition is intersecting iff no two parts are disjoint. The weight of a multiset partition is the sum of sizes of its parts. 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}}. The T_0 condition means the dual is strict.
%e A319782 Non-isomorphic representatives of the a(1) = 1 through a(4) = 7 multiset partitions:
%e A319782 1: {{1}}
%e A319782 2: {{1,1}}
%e A319782 3: {{1,1,1}}
%e A319782 {{1,2,2}}
%e A319782 {{1},{1,1}}
%e A319782 {{2},{1,2}}
%e A319782 4: {{1,1,1,1}}
%e A319782 {{1,2,2,2}}
%e A319782 {{1},{1,1,1}}
%e A319782 {{1},{1,2,2}}
%e A319782 {{2},{1,2,2}}
%e A319782 {{1,2},{2,2}}
%e A319782 {{1,3},{2,3}}
%Y A319782 Cf. A007716, A049311, A059201, A281116, A283877, A305843, A305854, A306006, A316980.
%Y A319782 Cf. A319755, A319759, A319760, A319765, A319779, A319787, A319789.
%K A319782 nonn,more
%O A319782 0,4
%A A319782 _Gus Wiseman_, Sep 27 2018