cp's OEIS Frontend

A369192 Number of labeled simple graphs with n vertices and at most n edges (not necessarily covering).

%I A369192 #11 Jul 15 2024 10:22:35
%S A369192 1,1,2,8,57,638,9949,198440,4791323,135142796,4346814276,156713948672,
%T A369192 6251579884084,273172369790743,12969420360339724,664551587744173992,
%U A369192 36543412829258260135,2146170890448154922648,134053014635659737513358,8872652968135849629240560
%N A369192 Number of labeled simple graphs with n vertices and at most n edges (not necessarily covering).
%F A369192 a(n) = Sum_{k=0..n} binomial(binomial(n,2),k).
%e A369192 The a(0) = 1 through a(3) = 8 graphs:
%e A369192   {}  {}  {}       {}
%e A369192           {{1,2}}  {{1,2}}
%e A369192                    {{1,3}}
%e A369192                    {{2,3}}
%e A369192                    {{1,2},{1,3}}
%e A369192                    {{1,2},{2,3}}
%e A369192                    {{1,3},{2,3}}
%e A369192                    {{1,2},{1,3},{2,3}}
%t A369192 Table[Length[Select[Subsets[Subsets[Range[n],{2}]], Length[#]<=n&]],{n,0,5}]
%o A369192 (Python)
%o A369192 from math import comb
%o A369192 def A369192(n): return sum(comb(comb(n,2),k) for k in range(n+1)) # _Chai Wah Wu_, Jul 14 2024
%Y A369192 The version for loop-graphs is A066383, covering A369194.
%Y A369192 The case of equality is A116508, covering A367863, also A367862.
%Y A369192 The connected case is A129271, unlabeled A005703.
%Y A369192 The covering case is A369191, minimal case A053530.
%Y A369192 Counting only covered vertices gives A369193.
%Y A369192 A006125 counts graphs, unlabeled A000088.
%Y A369192 A006129 counts covering graphs, unlabeled A002494.
%Y A369192 A054548 counts graphs covering n vertices with k edges, with loops A369199.
%Y A369192 A133686 counts choosable graphs, covering A367869.
%Y A369192 A367867 counts non-choosable graphs, covering A367868.
%Y A369192 Cf. A000169, A000272, A000666, A001187, A006649, A057500, A143543.
%K A369192 nonn
%O A369192 0,3
%A A369192 _Gus Wiseman_, Jan 17 2024