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%I #14 Jun 21 2019 22:44:02
%S 0,0,4,408,64528
%N Number of nesting labeled digraphs with vertices {1..n}.
%C Two edges (a,b), (c,d) are nesting if a < c and b > d or a > c and b < d.
%C Also unsortable digraphs with vertices {1..n}, where a digraph is sortable if, when the edges are listed in lexicographic order, their targets are weakly increasing.
%C Also the number of semicrossing digraphs with vertices {1..n}, where two edges (a,b), (c,d) are semicrossing if a < c and b < d or a > c and b > d. For example, the a(2) = 4 semicrossing digraph edge-sets are:
%C {11,22}
%C {11,12,22}
%C {11,21,22}
%C {11,12,21,22}
%F A002416(n) = a(n) + A326237(n).
%e The a(2) = 4 nesting digraph edge-sets:
%e {12,21}
%e {11,12,21}
%e {12,21,22}
%e {11,12,21,22}
%t Table[Length[Select[Subsets[Tuples[Range[n],2]],!OrderedQ[Last/@#]&]],{n,4}]
%Y Non-nesting digraphs are A326237.
%Y Nesting set partitions are A016098.
%Y MM-numbers of nesting multiset partitions are A326256.
%Y MM-numbers of unsortable multiset partitions are A326258.
%Y Cf. A000108, A001519, A002416, A229865.
%Y Cf. A326210, A326211, A326243, A326246, A326248, A326250.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Jun 19 2019
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