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 A320665 #13 Jan 28 2024 20:56:53
%S A320665 1,0,1,1,5,6,27,47,169,406,1327,3790,12560,39919,136821,470589,
%T A320665 1687981,6162696,23173374,88981796,349969596,1405386733,5764142220,
%U A320665 24111709328,102825231702,446665313598,1975339030948,8888051121242,40667889052853,189126710033882,893526261542899
%N A320665 Number of non-isomorphic multiset partitions of weight n with no singletons or vertices that appear only once.
%C A320665 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}}. This sequence counts non-isomorphic multiset partitions with no singletons whose dual also has no singletons.
%H A320665 Andrew Howroyd, <a href="/A320665/b320665.txt">Table of n, a(n) for n = 0..50</a>
%e A320665 Non-isomorphic representatives of the a(2) = 1 through a(6) = 27 multiset partitions:
%e A320665 {{1,1}} {{1,1,1}} {{1,1,1,1}} {{1,1,1,1,1}} {{1,1,1,1,1,1}}
%e A320665 {{1,1,2,2}} {{1,1,2,2,2}} {{1,1,1,2,2,2}}
%e A320665 {{1,1},{1,1}} {{1,1},{1,1,1}} {{1,1,2,2,2,2}}
%e A320665 {{1,1},{2,2}} {{1,1},{1,2,2}} {{1,1,2,2,3,3}}
%e A320665 {{1,2},{1,2}} {{1,1},{2,2,2}} {{1,1},{1,1,1,1}}
%e A320665 {{1,2},{1,2,2}} {{1,1,1},{1,1,1}}
%e A320665 {{1,1},{1,2,2,2}}
%e A320665 {{1,1,1},{2,2,2}}
%e A320665 {{1,1,2},{1,2,2}}
%e A320665 {{1,1},{2,2,2,2}}
%e A320665 {{1,1,2},{2,2,2}}
%e A320665 {{1,1},{2,2,3,3}}
%e A320665 {{1,1,2},{2,3,3}}
%e A320665 {{1,2},{1,1,2,2}}
%e A320665 {{1,2},{1,2,2,2}}
%e A320665 {{1,2},{1,2,3,3}}
%e A320665 {{1,2,2},{1,2,2}}
%e A320665 {{1,2,3},{1,2,3}}
%e A320665 {{2,2},{1,1,2,2}}
%e A320665 {{1,1},{1,1},{1,1}}
%e A320665 {{1,1},{1,2},{2,2}}
%e A320665 {{1,1},{2,2},{2,2}}
%e A320665 {{1,1},{2,2},{3,3}}
%e A320665 {{1,1},{2,3},{2,3}}
%e A320665 {{1,2},{1,2},{1,2}}
%e A320665 {{1,2},{1,2},{2,2}}
%e A320665 {{1,2},{1,3},{2,3}}
%o A320665 (PARI) \\ See links in A339645 for combinatorial species functions.
%o A320665 seq(n)={my(A=symGroupSeries(n)); NumUnlabeledObjsSeq(sCartProd(sExp(A-x*sv(1)), sExp(A-x*sv(1))))} \\ _Andrew Howroyd_, Jan 17 2023
%o A320665 (PARI) Vec(G(20,1)) \\ G defined in A369287. - _Andrew Howroyd_, Jan 28 2024
%Y A320665 Row sums of A369287.
%Y A320665 Cf. A001055, A007716, A306005, A317794, A318871, A320663, A320664, A321760.
%K A320665 nonn
%O A320665 0,5
%A A320665 _Gus Wiseman_, Oct 18 2018
%E A320665 Terms a(11) and beyond from _Andrew Howroyd_, Jan 17 2023