This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A319378 #6 Sep 19 2018 09:17:53
%S A319378 1,1,2,5,13,39,118,375,1225,4079,13794,47287,163962,573717,2023800
%N A319378 Number of plane trees with n nodes where the sequence of branches directly under any given node with at least two branches has empty intersection.
%e A319378 The a(5) = 13 locally nonintersecting plane trees:
%e A319378 ((((o)))) (((oo))) ((ooo)) (oooo)
%e A319378 (((o)o)) ((oo)o)
%e A319378 ((o(o))) (o(oo))
%e A319378 (((o))o) ((o)oo)
%e A319378 (o((o))) (o(o)o)
%e A319378 (oo(o))
%t A319378 monplane[n_]:=If[n==1,{{}},Join@@Table[Select[Tuples[monplane/@c],Or[Length[#]==1,Intersection@@#=={}]&],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
%t A319378 Table[Length[monplane[n]],{n,10}]
%Y A319378 Cf. A000081, A000108, A001003, A005043, A007562, A118376, A143363, A316470, A319122, A319379, A319380, A319381, A319436.
%K A319378 nonn,more
%O A319378 1,3
%A A319378 _Gus Wiseman_, Sep 17 2018