cp's OEIS Frontend

A369198 Number of labeled loop-graphs with n vertices and the same number of edges as covered vertices.

%I A369198 #8 Jan 20 2024 09:17:36
%S A369198 1,2,6,30,241,2759,40824,736342,15622835,380668095,10467815086,
%T A369198 320529284621,10813165015074,398413594789777,15917197015926392,
%U A369198 685312404706694574,31631317971844128229,1558017329350990780607,81567807853701988869120,4522975947689168088308305
%N A369198 Number of labeled loop-graphs with n vertices and the same number of edges as covered vertices.
%F A369198 Binomial transform of A368597.
%e A369198 The a(0) = 1 through a(3) = 30 loop-graphs (loops shown as singletons):
%e A369198   {}  {}     {}           {}
%e A369198       {{1}}  {{1}}        {{1}}
%e A369198              {{2}}        {{2}}
%e A369198              {{1},{2}}    {{3}}
%e A369198              {{1},{1,2}}  {{1},{2}}
%e A369198              {{2},{1,2}}  {{1},{3}}
%e A369198                           {{2},{3}}
%e A369198                           {{1},{1,2}}
%e A369198                           {{1},{1,3}}
%e A369198                           {{2},{1,2}}
%e A369198                           {{2},{2,3}}
%e A369198                           {{3},{1,3}}
%e A369198                           {{3},{2,3}}
%e A369198                           {{1},{2},{3}}
%e A369198                           {{1},{2},{1,3}}
%e A369198                           {{1},{2},{2,3}}
%e A369198                           {{1},{3},{1,2}}
%e A369198                           {{1},{3},{2,3}}
%e A369198                           {{2},{3},{1,2}}
%e A369198                           {{2},{3},{1,3}}
%e A369198                           {{1},{1,2},{1,3}}
%e A369198                           {{1},{1,2},{2,3}}
%e A369198                           {{1},{1,3},{2,3}}
%e A369198                           {{2},{1,2},{1,3}}
%e A369198                           {{2},{1,2},{2,3}}
%e A369198                           {{2},{1,3},{2,3}}
%e A369198                           {{3},{1,2},{1,3}}
%e A369198                           {{3},{1,2},{2,3}}
%e A369198                           {{3},{1,3},{2,3}}
%e A369198                           {{1,2},{1,3},{2,3}}
%t A369198 Table[Length[Select[Subsets[Subsets[Range[n],{1,2}]], Length[#]==Length[Union@@#]&]],{n,0,5}]
%Y A369198 The version counting all vertices is A014068.
%Y A369198 The loopless case is A367862, counting all vertices A116508.
%Y A369198 The covering case is A368597, connected A368951.
%Y A369198 With inequality we have A369196, covering A369194, connected A369197.
%Y A369198 A000085, A100861, A111924 count set partitions into singletons or pairs.
%Y A369198 A006125 counts simple graphs, also loop-graphs if shifted left.
%Y A369198 A006129 counts covering graphs, unlabeled A002494.
%Y A369198 A054548 counts graphs covering n vertices with k edges, with loops A369199.
%Y A369198 A322661 counts covering loop-graphs, unlabeled A322700.
%Y A369198 A368927 counts choosable loop-graphs, covering A369140.
%Y A369198 A369141 counts non-choosable loop-graphs, covering A369142.
%Y A369198 Cf. A000272, A000666, A006649, A062740, A066383, A367863, A369192, A369193.
%K A369198 nonn
%O A369198 0,2
%A A369198 _Gus Wiseman_, Jan 18 2024