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 A370169 #12 Feb 19 2024 22:56:17
%S A370169 1,1,3,7,19,48,135,373,1085,3184,9590,29258,90833,285352,908006,
%T A370169 2919953,9487330,31111997,102934602,343389708,1154684849,3912345408,
%U A370169 13353796977,45906197103,158915480378,553897148543,1943627750652,6865605601382,24411508473314,87364180212671,314682145679491
%N A370169 Number of unlabeled loop-graphs covering n vertices with at most n edges.
%H A370169 Andrew Howroyd, <a href="/A370169/b370169.txt">Table of n, a(n) for n = 0..50</a>
%e A370169 The a(0) = 1 through a(4) = 19 loop-graph edge sets (loops shown as singletons):
%e A370169 {} {{1}} {{1,2}} {{1},{2,3}} {{1,2},{3,4}}
%e A370169 {{1},{2}} {{1,2},{1,3}} {{1},{2},{3,4}}
%e A370169 {{1},{1,2}} {{1},{2},{3}} {{1},{1,2},{3,4}}
%e A370169 {{1},{2},{1,3}} {{1},{2,3},{2,4}}
%e A370169 {{1},{1,2},{1,3}} {{1},{2},{3},{4}}
%e A370169 {{1},{1,2},{2,3}} {{1,2},{1,3},{1,4}}
%e A370169 {{1,2},{1,3},{2,3}} {{1,2},{1,3},{2,4}}
%e A370169 {{1},{2},{3},{1,4}}
%e A370169 {{1},{2},{1,2},{3,4}}
%e A370169 {{1},{2},{1,3},{1,4}}
%e A370169 {{1},{2},{1,3},{2,4}}
%e A370169 {{1},{2},{1,3},{3,4}}
%e A370169 {{1},{1,2},{1,3},{1,4}}
%e A370169 {{1},{1,2},{1,3},{2,4}}
%e A370169 {{1},{1,2},{2,3},{2,4}}
%e A370169 {{1},{1,2},{2,3},{3,4}}
%e A370169 {{1},{2,3},{2,4},{3,4}}
%e A370169 {{1,2},{1,3},{1,4},{2,3}}
%e A370169 {{1,2},{1,3},{2,4},{3,4}}
%t A370169 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 A370169 Table[Length[Union[brute /@ Select[Subsets[Subsets[Range[n],{1,2}]], Union@@#==Range[n]&&Length[#]<=n&]]],{n,0,5}]
%o A370169 (PARI) \\ G defined in A070166.
%o A370169 a(n)=my(A=O(x*x^n)); if(n==0, 1, polcoef((G(n,A)-G(n-1,A))/(1-x), n)) \\ _Andrew Howroyd_, Feb 19 2024
%Y A370169 The case of equality is A368599, covering case of A368598.
%Y A370169 The labeled version is A369194, covering case of A066383.
%Y A370169 This is the covering case of A370168.
%Y A370169 The loopless version is the covering case of A370315, labeled A369192.
%Y A370169 This is the loopless version is A370316, labeled A369191.
%Y A370169 A006125 counts graphs, unlabeled A000088.
%Y A370169 A006129 counts covering graphs, unlabeled A002494.
%Y A370169 A322661 counts covering loop-graphs, unlabeled A322700.
%Y A370169 Cf. A000666, A005703, A014068, A062740, A116508, A368597, A368927, A369141, A369196, A369197, A369199.
%K A370169 nonn
%O A370169 0,3
%A A370169 _Gus Wiseman_, Feb 16 2024
%E A370169 a(7) onwards from _Andrew Howroyd_, Feb 19 2024