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 A370166 #5 Feb 12 2024 08:34:39
%S A370166 1,1,3,9,36,180,1313,14709,277755,9304977,568315345,63806703305,
%T A370166 13200565313255,5042653259803433,3567050969262370941,
%U A370166 4688444463558713135201,11491940559865490367844649,52719458629883487816297211441,454220675869975957947658748125099
%N A370166 Number of unlabeled loop-graphs covering n vertices without a non-loop edge with loops at both ends.
%F A370166 First differences of A339832 (the non-covering version).
%e A370166 Representatives of the a(0) = 1 through a(3) = 9 loop-graphs (loops shown as singletons):
%e A370166 {} {{1}} {{1,2}} {{1},{2,3}}
%e A370166 {{1},{2}} {{1,2},{1,3}}
%e A370166 {{1},{1,2}} {{1},{2},{3}}
%e A370166 {{1},{2},{1,3}}
%e A370166 {{1},{1,2},{1,3}}
%e A370166 {{1},{1,2},{2,3}}
%e A370166 {{1,2},{1,3},{2,3}}
%e A370166 {{1},{2},{1,3},{2,3}}
%e A370166 {{1},{1,2},{1,3},{2,3}}
%t A370166 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 A370166 Table[Length[Union[brute /@ Select[Subsets[Subsets[Range[n],{1,2}]],Union@@#==Range[n] && !MatchQ[#,{___,{x_},___,{y_},___,{x_,y_},___}]&]]], {n,0,4}]
%Y A370166 Without loops we have A002494, labeled A006129, connected A001349.
%Y A370166 The non-covering version is A339832.
%Y A370166 The labeled version is A370165, non-covering A079491 (apparently).
%Y A370166 A000666 counts unlabeled loop-graphs, covering A322700.
%Y A370166 A006125 counts labeled loop-graphs (shifted left), covering A322661.
%Y A370166 Cf. A000085, A001187, A048291, A062740, A116539.
%K A370166 nonn
%O A370166 0,3
%A A370166 _Gus Wiseman_, Feb 12 2024