OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..24
E. A. Bender and E. R. Canfield, The asymptotic number of labeled graphs with given degree sequences, Journal of Combinatorial Theory, Series A, 24 (1978), 296-307.
Andrew Howroyd, PARI Program
Atabey Kaygun, Enumerating Labeled Graphs that Realize a Fixed Degree Sequence, arXiv:2101.02299 [math.CO], 2021.
B. D. McKay, Applications of a technique for labelled enumeration, Congress. Numerantium, 40 (1983), 207-221.
Wikipedia, Regular graph
EXAMPLE
From Gus Wiseman, Dec 19 2018: (Start)
A graph is regular if all vertices have the same degree. For example, the a(4) = 8 simple regular graphs are:
1 2
3 4
.
4---1 3---1 2---1
3---2 4---2 4---3
.
3---4 4---3 4---2
| | | | | |
1---2 1---2 1---3
.
4---3
| X |
2---1
(End)
MATHEMATICA
Table[Sum[SeriesCoefficient[Product[1+Times@@x/@s, {s, Subsets[Range[n], {2}]}], Sequence@@Table[{x[i], 0, k}, {i, n}]], {k, 0, n-1}], {n, 1, 9}] (* Gus Wiseman, Dec 19 2018 *)
PROG
(PARI) \\ See link for program file.
for(n=1, 10, print1(A295193(n), ", ")) \\ Andrew Howroyd, Aug 28 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Álvar Ibeas, Nov 16 2017
EXTENSIONS
a(16)-a(18) from Andrew Howroyd, Aug 28 2019
STATUS
approved