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 A322118 #9 Feb 07 2021 19:42:39
%S A322118 1,1,2,3,7,11,29,55,155,386,1171
%N A322118 Number of non-isomorphic connected multiset partitions of weight n with no singletons that cannot be capped by a tree.
%C A322118 The density of a multiset partition is defined to be the sum of numbers of distinct elements in each part, minus the number of parts, minus the total number of distinct elements in the whole partition. A multiset partition is a tree if it has more than one part, is connected, and has density -1. A cap is a certain kind of non-transitive coarsening of a multiset partition. For example, the four caps of {{1,1},{1,2},{2,2}} are {{1,1},{1,2},{2,2}}, {{1,1},{1,2,2}}, {{1,1,2},{2,2}}, {{1,1,2,2}}. - _Gus Wiseman_, Feb 05 2021
%H A322118 Gus Wiseman, <a href="http://www.mathematica-journal.com/2017/12/every-clutter-is-a-tree-of-blobs/">Every Clutter Is a Tree of Blobs</a>, The Mathematica Journal, Vol. 19, 2017.
%e A322118 The multiset partition C = {{1,1},{1,2,3},{2,3,3}} is not a tree but has the cap {{1,1},{1,2,3,3}} which is a tree, so C is not counted under a(8).
%e A322118 Non-isomorphic representatives of the a(2) = 2 through a(6) = 29 multiset partitions:
%e A322118 {{1,1}} {{1,1,1}} {{1,1,1,1}} {{1,1,1,1,1}} {{1,1,1,1,1,1}}
%e A322118 {{1,2}} {{1,2,2}} {{1,1,2,2}} {{1,1,2,2,2}} {{1,1,1,2,2,2}}
%e A322118 {{1,2,3}} {{1,2,2,2}} {{1,2,2,2,2}} {{1,1,2,2,2,2}}
%e A322118 {{1,2,3,3}} {{1,2,2,3,3}} {{1,1,2,2,3,3}}
%e A322118 {{1,2,3,4}} {{1,2,3,3,3}} {{1,2,2,2,2,2}}
%e A322118 {{1,1},{1,1}} {{1,2,3,4,4}} {{1,2,2,3,3,3}}
%e A322118 {{1,2},{1,2}} {{1,2,3,4,5}} {{1,2,3,3,3,3}}
%e A322118 {{1,1},{1,1,1}} {{1,2,3,3,4,4}}
%e A322118 {{1,2},{1,2,2}} {{1,2,3,4,4,4}}
%e A322118 {{2,2},{1,2,2}} {{1,2,3,4,5,5}}
%e A322118 {{2,3},{1,2,3}} {{1,2,3,4,5,6}}
%e A322118 {{1,1},{1,1,1,1}}
%e A322118 {{1,1,1},{1,1,1}}
%e A322118 {{1,1,2},{1,2,2}}
%e A322118 {{1,2},{1,1,2,2}}
%e A322118 {{1,2},{1,2,2,2}}
%e A322118 {{1,2},{1,2,3,3}}
%e A322118 {{1,2,2},{1,2,2}}
%e A322118 {{1,2,3},{1,2,3}}
%e A322118 {{1,2,3},{2,3,3}}
%e A322118 {{1,3,4},{2,3,4}}
%e A322118 {{2,2},{1,1,2,2}}
%e A322118 {{2,2},{1,2,2,2}}
%e A322118 {{2,3},{1,2,3,3}}
%e A322118 {{3,3},{1,2,3,3}}
%e A322118 {{3,4},{1,2,3,4}}
%e A322118 {{1,1},{1,1},{1,1}}
%e A322118 {{1,2},{1,2},{1,2}}
%e A322118 {{1,2},{1,3},{2,3}}
%Y A322118 Non-isomorphic tree multiset partitions are counted by A321229, or A321231 without singletons.
%Y A322118 The version with singletons is A322110.
%Y A322118 The weak-antichain case is counted by A322138, or A322117 with singletons.
%Y A322118 Cf. A002218, A007718, A013922, A030019, A275307, A293994, A304118, A304382, A304887, A305079, A319719, A319721, A321194.
%K A322118 nonn,more
%O A322118 0,3
%A A322118 _Gus Wiseman_, Nov 26 2018
%E A322118 Definition corrected by _Gus Wiseman_, Feb 05 2021