OFFSET
0,2
COMMENTS
A directed edge (a,b) is increasing if a < b. Two edges (a,b), (c,d) are crossing if a < c < b < d or c < a < d < b.
Conjecture: Also the number of non-nesting digraphs with vertices {1..n} whose increasing edges are not crossing, where two edges (a,b), (c,d) are nesting if a < c < d < b or c < a < b < d.
FORMULA
a(n) = 2^(n * (n + 1)/2) * A054726(n).
MATHEMATICA
croXQ[eds_]:=MatchQ[eds, {___, {x_, y_}, ___, {z_, t_}, ___}/; x<z<y<t||z<x<t<y];
Table[Length[Select[Subsets[Tuples[Range[n], 2]], !croXQ[#]&]], {n, 0, 4}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 30 2019
STATUS
approved