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.
LINKS
Wikipedia, Regular graph
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