cp's OEIS Frontend

A322555 Number of labeled simple graphs on n vertices where all non-isolated vertices have the same degree.

%I A322555 #12 May 21 2020 16:11:20
%S A322555 1,1,2,5,18,69,390,2703,59474,1548349,168926258,12165065351,
%T A322555 7074423247562,2294426405580191,4218009215702391954,
%U A322555 3810376434461484994317,35102248193591661086921250,156873334244228518638713087133,4144940994226400702145709978234154
%N A322555 Number of labeled simple graphs on n vertices where all non-isolated vertices have the same degree.
%C A322555 Such graphs may be said to have regular support.
%F A322555 a(n) = 1 + Sum_{k=1..n} binomial(n, k)*(A295193(k) - 1). - _Andrew Howroyd_, Dec 17 2018
%e A322555 The a(4) = 18 edge sets:
%e A322555   {}
%e A322555   {{1,2}}
%e A322555   {{1,3}}
%e A322555   {{1,4}}
%e A322555   {{2,3}}
%e A322555   {{2,4}}
%e A322555   {{3,4}}
%e A322555   {{1,2},{3,4}}
%e A322555   {{1,3},{2,4}}
%e A322555   {{1,4},{2,3}}
%e A322555   {{1,2},{1,3},{2,3}}
%e A322555   {{1,2},{1,4},{2,4}}
%e A322555   {{1,3},{1,4},{3,4}}
%e A322555   {{2,3},{2,4},{3,4}}
%e A322555   {{1,2},{1,3},{2,4},{3,4}}
%e A322555   {{1,2},{1,4},{2,3},{3,4}}
%e A322555   {{1,3},{1,4},{2,3},{2,4}}
%e A322555   {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}
%t A322555 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],SameQ@@Length/@Split[Sort[Join@@#]]&]],{n,6}]
%Y A322555 Cf. A000569, A005176, A038041, A059441, A295193, A306017, A306019, A319169, A320458.
%K A322555 nonn
%O A322555 0,3
%A A322555 _Gus Wiseman_, Dec 15 2018
%E A322555 a(8)-a(15) from _Andrew Howroyd_, Dec 17 2018
%E A322555 a(16)-a(18) from _Andrew Howroyd_, May 21 2020