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A322698 Number of regular graphs with half-edges on n labeled vertices. 6

%I

%S 1,2,4,10,40,278,3554,84590,3776280,317806466,50710452574,

%T 15414839551538,8964708979273634,10008446308186072290,

%U 21518891146915893435358,89320970210116481106835986,717558285660687970023516336792,11176382741327158622885664697124082,338202509574712032788035618665293979610

%N Number of regular graphs with half-edges on n labeled vertices.

%C A graph is regular if all vertices have the same degree. A half-edge is like a loop except it only adds 1 to the degree of its vertex.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Regular_graph">Regular graph</a>

%e The a(3) = 10 edge sets:

%e {}

%e {{1},{2,3}}

%e {{3},{1,2}}

%e {{2},{1,3}}

%e {{1},{2},{3}}

%e {{1,2},{1,3},{2,3}}

%e {{1},{3},{1,2},{2,3}}

%e {{1},{2},{1,3},{2,3}}

%e {{2},{3},{1,2},{1,3}}

%e {{1},{2},{3},{1,2},{1,3},{2,3}}

%t Table[Sum[SeriesCoefficient[Product[1+Times@@x/@s,{s,Union/@Select[Tuples[Range[n],2],OrderedQ]}],Sequence@@Table[{x[i],0,k},{i,n}]],{k,0,n-1}],{n,1,6}]

%o (PARI) for(n=1, 10, print1(A322698(n), ", ")) \\ See A295193 for script, _Andrew Howroyd_, Aug 28 2019

%Y Row sums of A333157.

%Y Cf. A058891, A059441, A116539, A283877, A295193, A319189, A319190, A319612, A319729.

%K nonn

%O 0,2

%A _Gus Wiseman_, Dec 23 2018

%E a(10)-a(18) from _Andrew Howroyd_, Aug 28 2019

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Last modified April 10 02:39 EDT 2020. Contains 333392 sequences. (Running on oeis4.)