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 A369200 #12 Feb 02 2024 17:49:30
%S A369200 1,1,3,7,18,43,112,282,740,1940,5182,13916,37826,103391,284815,788636,
%T A369200 2195414,6137025,17223354,48495640,136961527,387819558,1100757411,
%U A369200 3130895452,8922294498,25470279123,72823983735,208515456498,597824919725,1716072103910,4931540188084
%N A369200 Number of unlabeled loop-graphs covering n vertices such that it is possible to choose a different vertex from each edge (choosable).
%C A369200 These are covering loop-graphs with at most one cycle (unicyclic) in each connected component.
%H A369200 Andrew Howroyd, <a href="/A369200/b369200.txt">Table of n, a(n) for n = 0..500</a>
%F A369200 First differences of A369145.
%F A369200 Euler transform of A369289 with A369289(1) = 1. - _Andrew Howroyd_, Feb 02 2024
%e A369200 Representatives of the a(1) = 1 through a(4) = 18 loop-graphs (loops shown as singletons):
%e A369200 {{1}} {{1,2}} {{1},{2,3}} {{1,2},{3,4}}
%e A369200 {{1},{2}} {{1,2},{1,3}} {{1},{2},{3,4}}
%e A369200 {{1},{1,2}} {{1},{2},{3}} {{1},{1,2},{3,4}}
%e A369200 {{1},{2},{1,3}} {{1},{2,3},{2,4}}
%e A369200 {{1},{1,2},{1,3}} {{1},{2},{3},{4}}
%e A369200 {{1},{1,2},{2,3}} {{1,2},{1,3},{1,4}}
%e A369200 {{1,2},{1,3},{2,3}} {{1,2},{1,3},{2,4}}
%e A369200 {{1},{2},{3},{1,4}}
%e A369200 {{1},{2},{1,3},{1,4}}
%e A369200 {{1},{2},{1,3},{2,4}}
%e A369200 {{1},{2},{1,3},{3,4}}
%e A369200 {{1},{1,2},{1,3},{1,4}}
%e A369200 {{1},{1,2},{1,3},{2,4}}
%e A369200 {{1},{1,2},{2,3},{2,4}}
%e A369200 {{1},{1,2},{2,3},{3,4}}
%e A369200 {{1},{2,3},{2,4},{3,4}}
%e A369200 {{1,2},{1,3},{1,4},{2,3}}
%e A369200 {{1,2},{1,3},{2,4},{3,4}}
%t A369200 brute[m_]:=First[Sort[Table[Sort[Sort /@ (m/.Rule@@@Table[{(Union@@m)[[i]],p[[i]]},{i,Length[p]}])], {p,Permutations[Range[Length[Union@@m]]]}]]];
%t A369200 Table[Length[Union[brute /@ Select[Subsets[Subsets[Range[n],{1,2}]], Union@@#==Range[n]&&Length[Select[Tuples[#], UnsameQ@@#&]]!=0&]]],{n,0,4}]
%Y A369200 Without the choice condition we have A322700, labeled A322661.
%Y A369200 Without loops we have A368834, covering case of A134964.
%Y A369200 For exactly n edges we have A368984, labeled A333331 (maybe).
%Y A369200 The labeled version is A369140, covering case of A368927.
%Y A369200 The labeled complement is A369142, covering case of A369141.
%Y A369200 This is the covering case of A369145.
%Y A369200 The complement is counted by A369147, covering case of A369146.
%Y A369200 The complement without loops is A369202, covering case of A140637.
%Y A369200 A000085, A100861, A111924 count set partitions into singletons or pairs.
%Y A369200 A000666 counts unlabeled loop-graphs, labeled A006125 (shifted left).
%Y A369200 A006129 counts covering graphs, unlabeled A002494.
%Y A369200 A007716 counts non-isomorphic multiset partitions, connected A007718.
%Y A369200 A129271 counts connected choosable simple graphs, unlabeled A005703.
%Y A369200 A133686 counts choosable labeled graphs, covering A367869.
%Y A369200 Cf. A000088, A000612, A006649, A014068, A055621, A137916, A137917, A368835, A369194, A369199.
%K A369200 nonn
%O A369200 0,3
%A A369200 _Gus Wiseman_, Jan 23 2024
%E A369200 a(7) onwards from _Andrew Howroyd_, Feb 02 2024