OFFSET
0,4
COMMENTS
The axiom of choice says that, given any set of nonempty sets Y, it is possible to choose a set containing an element from each. The strict version requires this set to have the same cardinality as Y, meaning no element is chosen more than once.
Number of labeled n-node graphs with at most one cycle in each component and no isolated vertices. - Andrew Howroyd, Dec 30 2023
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: exp(B(x) - x - 1) where B(x) is the e.g.f. of A129271. - Andrew Howroyd, Dec 30 2023
EXAMPLE
The a(3) = 4 graphs:
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,3},{2,3}}
{{1,2},{1,3},{2,3}}
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Union@@#==Range[n]&&Select[Tuples[#], UnsameQ@@#&]!={}&]], {n, 0, 5}]
PROG
(PARI) seq(n)={my(t=-lambertw(-x + O(x*x^n))); Vec(serlaplace(sqrt(1/(1-t))*exp(t/2 - 3*t^2/4 - x)))} \\ Andrew Howroyd, Dec 30 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 08 2023
EXTENSIONS
Terms a(7) and beyond from Andrew Howroyd, Dec 30 2023
STATUS
approved