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 A319380 #6 Sep 19 2018 09:18:06
%S A319380 1,1,1,2,3,5,9,17,30,53,94,169,303,543,968,1728,3080,5491,9776,17415,
%T A319380 31008
%N A319380 Number of plane trees with n nodes where the sequence of branches directly under any given node is a chain of distinct multisets.
%H A319380 Gus Wiseman, <a href="/A319380/a319380.png">The a(12) = 169 identity chain trees.</a>
%e A319380 The a(8) = 17 locally identity chain trees:
%e A319380 (((((((o))))))) (((((o(o)))))) (((o(o(o))))) (o(o(o(o))))
%e A319380 ((((o((o)))))) ((o((o(o))))) (o(o)(o(o)))
%e A319380 (((o(((o)))))) ((o(o((o)))))
%e A319380 ((o((((o)))))) (((o)(o(o))))
%e A319380 (o(((((o)))))) (o(((o(o)))))
%e A319380 (o((o((o)))))
%e A319380 (o(o(((o)))))
%e A319380 ((o)(o((o))))
%e A319380 (((o))(o(o)))
%t A319380 submultisetQ[M_,N_]:=Or[Length[M]==0,MatchQ[{Sort[List@@M],Sort[List@@N]},{{x_,Z___},{___,x_,W___}}/;submultisetQ[{Z},{W}]]];
%t A319380 idchnplane[n_]:=If[n==1,{{}},Join@@Table[Select[Tuples[idchnplane/@c],And[UnsameQ@@#,And@@submultisetQ@@@Partition[#,2,1]]&],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
%t A319380 Table[Length[idchnplane[n]],{n,10}]
%Y A319380 Cf. A000081, A000108, A001003, A005043, A007562, A118376, A316470, A319122, A319379, A319381.
%K A319380 nonn,more
%O A319380 1,4
%A A319380 _Gus Wiseman_, Sep 17 2018