cp's OEIS Frontend

A369194 Number of labeled loop-graphs covering n vertices with at most n edges.

%I A369194 #13 Mar 23 2024 22:13:13
%S A369194 1,1,4,23,199,2313,34015,606407,12712643,306407645,8346154699,
%T A369194 253476928293,8490863621050,310937199521774,12356288017546937,
%U A369194 529516578044589407,24339848939829286381,1194495870124420574751,62332449791125883072149,3446265450868329833016605
%N A369194 Number of labeled loop-graphs covering n vertices with at most n edges.
%C A369194 Row-sums of left portion of A369199.
%F A369194 Inverse binomial transform of A369196.
%e A369194 The a(0) = 1 through a(3) = 23 loop-graphs (loops shown as singletons):
%e A369194   {}  {{1}}  {{1,2}}      {{1},{2,3}}
%e A369194              {{1},{2}}    {{2},{1,3}}
%e A369194              {{1},{1,2}}  {{3},{1,2}}
%e A369194              {{2},{1,2}}  {{1,2},{1,3}}
%e A369194                           {{1,2},{2,3}}
%e A369194                           {{1},{2},{3}}
%e A369194                           {{1,3},{2,3}}
%e A369194                           {{1},{2},{1,3}}
%e A369194                           {{1},{2},{2,3}}
%e A369194                           {{1},{3},{1,2}}
%e A369194                           {{1},{3},{2,3}}
%e A369194                           {{2},{3},{1,2}}
%e A369194                           {{2},{3},{1,3}}
%e A369194                           {{1},{1,2},{1,3}}
%e A369194                           {{1},{1,2},{2,3}}
%e A369194                           {{1},{1,3},{2,3}}
%e A369194                           {{2},{1,2},{1,3}}
%e A369194                           {{2},{1,2},{2,3}}
%e A369194                           {{2},{1,3},{2,3}}
%e A369194                           {{3},{1,2},{1,3}}
%e A369194                           {{3},{1,2},{2,3}}
%e A369194                           {{3},{1,3},{2,3}}
%e A369194                           {{1,2},{1,3},{2,3}}
%t A369194 Table[Length[Select[Subsets[Subsets[Range[n],{1,2}]], Length[Union@@#]==n&&Length[#]<=n&]],{n,0,5}]
%Y A369194 The minimal case is A001862, without loops A053530.
%Y A369194 This is the covering case of A066383 and A369196, cf. A369192 and A369193.
%Y A369194 The case of equality is A368597, without loops A367863.
%Y A369194 The version without loops is A369191.
%Y A369194 The connected case is A369197, without loops A129271.
%Y A369194 The unlabeled version is A370169, equality A368599, non-covering A368598.
%Y A369194 A000085, A100861, A111924 count set partitions into singletons or pairs.
%Y A369194 A006125 counts simple graphs; also loop-graphs if shifted left.
%Y A369194 A006129 counts covering graphs, unlabeled A002494.
%Y A369194 A054548 counts graphs covering n vertices with k edges, with loops A369199.
%Y A369194 A133686 counts choosable graphs, covering A367869.
%Y A369194 A322661 counts covering loop-graphs, unlabeled A322700.
%Y A369194 A367867 counts non-choosable graphs, covering A367868.
%Y A369194 A368927 counts choosable loop-graphs, covering A369140.
%Y A369194 A369141 counts non-choosable loop-graphs, covering A369142.
%Y A369194 Cf. A000169, A000272, A000666, A003465, A005703, A006649, A057500, A062740, A116508, A367862, A367916.
%K A369194 nonn
%O A369194 0,3
%A A369194 _Gus Wiseman_, Jan 17 2024