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%I #16 Sep 02 2019 23:03:50
%S 1,1,1,4,13,146,826,44808,1074557,155741296,10381741786,6939251270348,
%T 2203360264480750,4186526735251514044,3747344007864300197810,
%U 35041787059621536192399824,156277111373298355107598128061,4142122641757597729416733678931968
%N Number of connected regular simple graphs on n labeled vertices.
%C A graph is regular if all vertices have the same degree.
%H Gus Wiseman, <a href="/A322659/a322659.png">The a(5) = 13 connected regular simple graphs.</a>
%H Gus Wiseman, <a href="/A322659/a322659_1.png">The a(6) = 146 connected regular simple graphs.</a>
%t 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 Table[If[n==1,1,Length[Select[Subsets[Subsets[Range[n],{2}]],And[Union@@#==Range[n],SameQ@@Length/@Split[Sort[Join@@#]],Length[csm[#]]==1]&]]],{n,6}]
%Y Row sums of A324163.
%Y Cf. A054921, A059441, A062740, A295193, A299353, A305078, A319190, A319612, A319729, A322635.
%K nonn
%O 1,4
%A _Gus Wiseman_, Dec 22 2018
%E a(8)-a(15) from _Andrew Howroyd_, Dec 23 2018
%E a(16)-a(18) from _Andrew Howroyd_, Sep 02 2019
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