login
A322698
Number of regular graphs with half-edges on n labeled vertices.
6
1, 2, 4, 10, 40, 278, 3554, 84590, 3776280, 317806466, 50710452574, 15414839551538, 8964708979273634, 10008446308186072290, 21518891146915893435358, 89320970210116481106835986, 717558285660687970023516336792, 11176382741327158622885664697124082, 338202509574712032788035618665293979610
OFFSET
0,2
COMMENTS
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.
EXAMPLE
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}}
MATHEMATICA
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}]
PROG
(PARI) for(n=1, 10, print1(A322698(n), ", ")) \\ See A295193 for script, Andrew Howroyd, Aug 28 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 23 2018
EXTENSIONS
a(10)-a(18) from Andrew Howroyd, Aug 28 2019
STATUS
approved