cp's OEIS Frontend

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.

A327070 Number of non-connected simple labeled graphs covering n vertices.

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%I A327070 #8 Sep 11 2019 20:21:34
%S A327070 1,0,0,0,3,40,745,21028,973889,80133088,12523299729,3847333778244,
%T A327070 2341705361100633,2821794389863015840,6728707109106848947081,
%U A327070 31769173063866390661714996,297278309767391164611330317921
%N A327070 Number of non-connected simple labeled graphs covering n vertices.
%C A327070 We consider the empty graph to be neither connected (one component) nor disconnected (more than one component).
%F A327070 a(n) = A006129(n) - A001187(n), if we assume A001187(0) = 0 and A001187(1) = 0.
%F A327070 Inverse binomial transform of A327199.
%e A327070 The a(4) = 3 graphs:
%e A327070   {{1,2},{3,4}}
%e A327070   {{1,3},{2,4}}
%e A327070   {{1,4},{2,3}}
%t A327070 csm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[OrderedQ[#],UnsameQ@@#,Length[Intersection@@s[[#]]]>0]&]},If[c=={},s,csm[Sort[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
%t A327070 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],Union@@#==Range[n]&&Length[csm[#]]!=1&]],{n,0,5}]
%Y A327070 Column k = 0 of A327149.
%Y A327070 The unlabeled version is A327075.
%Y A327070 The non-covering version is A327199.
%Y A327070 Cf. A000719, A001187, A001349, A002494, A006125, A006129, A054592, A327070.
%K A327070 nonn
%O A327070 0,5
%A A327070 _Gus Wiseman_, Aug 24 2019