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A322698
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Number of regular graphs with half-edges on n labeled vertices.
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6
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1, 2, 4, 10, 40, 278, 3554, 84590, 3776280, 317806466, 50710452574, 15414839551538, 8964708979273634, 10008446308186072290, 21518891146915893435358, 89320970210116481106835986, 717558285660687970023516336792, 11176382741327158622885664697124082, 338202509574712032788035618665293979610
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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The a(3) = 10 edge sets:
{}
{{1},{2,3}}
{{3},{1,2}}
{{2},{1,3}}
{{1},{2},{3}}
{{1,2},{1,3},{2,3}}
{{1},{3},{1,2},{2,3}}
{{1},{2},{1,3},{2,3}}
{{2},{3},{1,2},{1,3}}
{{1},{2},{3},{1,2},{1,3},{2,3}}
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MATHEMATICA
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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}]
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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