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%I A369196 #9 Jan 18 2024 04:40:49
%S A369196 1,2,7,39,320,3584,51405,900947,18661186,445827942,12062839691,
%T A369196 364451604095,12157649050827,443713171974080,17583351295466338,
%U A369196 751745326170662049,34485624653535808340,1689485711682987916502,88030098291829749593643,4860631073631586486397141
%N A369196 Number of labeled loop-graphs with n vertices and at most as many edges as covered vertices.
%F A369196 Binomial transform of A369194.
%e A369196 The a(0) = 1 through a(2) = 7 loop-graphs:
%e A369196   {}  {}     {}
%e A369196       {{1}}  {{1}}
%e A369196              {{2}}
%e A369196              {{1,2}}
%e A369196              {{1},{2}}
%e A369196              {{1},{1,2}}
%e A369196              {{2},{1,2}}
%t A369196 Table[Length[Select[Subsets[Subsets[Range[n],{1,2}]],Length[#]<=Length[Union@@#]&]],{n,0,5}]
%Y A369196 The version counting all vertices is A066383, without loops A369192.
%Y A369196 The loopless case is A369193, with case of equality A367862.
%Y A369196 The covering case is A369194, connected A369197, minimal case A001862.
%Y A369196 The case of equality is A369198, covering case A368597.
%Y A369196 A000085, A100861, A111924 count set partitions into singletons or pairs.
%Y A369196 A006125 counts simple graphs, also loop-graphs if shifted left.
%Y A369196 A006129 counts covering graphs, unlabeled A002494.
%Y A369196 A054548 counts graphs covering n vertices with k edges, with loops A369199.
%Y A369196 A322661 counts covering loop-graphs, unlabeled A322700.
%Y A369196 A368927 counts choosable loop-graphs, covering A369140.
%Y A369196 A369141 counts non-choosable loop-graphs, covering A369142.
%Y A369196 Cf. A000169, A000272, A000666, A001187, A006649, A057500, A062740, A116508, A367863, A369145.
%K A369196 nonn
%O A369196 0,2
%A A369196 _Gus Wiseman_, Jan 17 2024

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