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 A319381 #7 Sep 19 2018 09:18:12
%S A319381 1,1,1,2,2,4,6,9,11,20,28,40,58,82,110,159,217,305,420,570,767,1042
%N A319381 Number of plane trees with n nodes where the sequence of branches directly under any given node is a membership-chain.
%H A319381 Gus Wiseman, <a href="/A319381/a319381.png">The a(15) = 110 membership-chain trees.</a>
%e A319381 The a(9) = 11 membership-chain trees:
%e A319381 ((((((((o)))))))) (((((((o)o)))))) ((((((o)o)o)))) (((((o)o)o)o))
%e A319381 ((((((o))(o))))) (((((o)o)(o)))) ((((o)o)(o)o))
%e A319381 (((((o)))((o)))) (((((o))(o)o))) ((((o))(o)o)o)
%e A319381 ((((o))(o))(o))
%t A319381 yanplane[n_]:=If[n==1,{{}},Join@@Table[Select[Tuples[yanplane/@c],And@@MemberQ@@@Partition[#,2,1]&],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
%t A319381 Table[Length[yanplane[n]],{n,10}]
%Y A319381 Cf. A000081, A000108, A001003, A005043, A007562, A118376, A316470, A319122, A319379, A319380, A319436.
%K A319381 nonn,more
%O A319381 1,4
%A A319381 _Gus Wiseman_, Sep 17 2018