OFFSET
0,2
COMMENTS
These are loop-graphs where every connected component has a number of edges less than or equal to the number of vertices. Also loop-graphs with at most one cycle (unicyclic) in each connected component.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
FORMULA
Binomial transform of A369140.
E.g.f.: exp(3*T(x)/2 - 3*T(x)^2/4)/sqrt(1-T(x)), where T(x) is the e.g.f. of A000169. - Andrew Howroyd, Feb 02 2024
EXAMPLE
The a(0) = 1 through a(2) = 7 loop-graphs (loops shown as singletons):
{} {} {}
{{1}} {{1}}
{{2}}
{{1,2}}
{{1},{2}}
{{1},{1,2}}
{{2},{1,2}}
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {1, 2}]], Length[Select[Tuples[#], UnsameQ@@#&]]!=0&]], {n, 0, 5}]
PROG
(PARI) seq(n)={my(t=-lambertw(-x + O(x*x^n))); Vec(serlaplace(exp(3*t/2 - 3*t^2/4)/sqrt(1-t) ))} \\ Andrew Howroyd, Feb 02 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 15 2024
EXTENSIONS
a(7) onwards from Andrew Howroyd, Feb 02 2024
STATUS
approved