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 A319379 #7 Sep 19 2018 09:18:00
%S A319379 1,1,2,4,9,19,43,93,207,452,997,2176,4776,10418,22781,49674,108421
%N A319379 Number of plane trees with n nodes where the sequence of branches directly under any given node is a chain of multisets.
%H A319379 Gus Wiseman, <a href="/A319379/a319379.png">The a(9) = 207 chain trees.</a>
%e A319379 The a(6) = 19 chain trees:
%e A319379 (((((o))))) ((((oo)))) (((ooo))) ((oooo)) (ooooo)
%e A319379 (((o)(o))) ((o)(oo)) (o(ooo))
%e A319379 (((o(o)))) ((o(oo))) (oo(oo))
%e A319379 ((o((o)))) ((oo(o))) (ooo(o))
%e A319379 (o(((o)))) (o((oo)))
%e A319379 (o(o)(o))
%e A319379 (o(o(o)))
%e A319379 (oo((o)))
%t A319379 submultisetQ[M_,N_]:=Or[Length[M]==0,MatchQ[{Sort[List@@M],Sort[List@@N]},{{x_,Z___},{___,x_,W___}}/;submultisetQ[{Z},{W}]]];
%t A319379 chnplane[n_]:=If[n==1,{{}},Join@@Table[Select[Tuples[chnplane/@c],And@@submultisetQ@@@Partition[#,2,1]&],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
%t A319379 Table[Length[chnplane[n]],{n,10}]
%Y A319379 Cf. A000081, A000108, A001003, A005043, A007562, A118376, A143363, A316470, A319122, A319378, A319380, A319381.
%K A319379 nonn,more
%O A319379 1,3
%A A319379 _Gus Wiseman_, Sep 17 2018