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 A124346 #14 Jan 26 2018 12:00:44
%S A124346 1,1,1,2,2,4,6,11,17,32,56,102,184,340,624,1161,2156,4036,7562,14234,
%T A124346 26828,50747,96125,182545,347187,661618,1262583,2413275,4618571,
%U A124346 8850905,16981142,32616900,62713951,120703497,232527392,448344798,865182999,1670884073
%N A124346 Number of rooted identity trees on n nodes with thinning limbs.
%C A124346 A rooted tree with thinning limbs is such that if a node has k children, all its children have at most k children.
%H A124346 Alois P. Heinz, <a href="/A124346/b124346.txt">Table of n, a(n) for n = 1..140</a>
%e A124346 The a(7) = 6 trees are ((((((o)))))), (o((((o))))), (o(o((o)))), ((o)(((o)))), ((o)(o(o))), (o(o)((o))). - _Gus Wiseman_, Jan 25 2018
%t A124346 idthinQ[t_]:=And@@Cases[t,b_List:>UnsameQ@@b&&Length[b]>=Max@@Length/@b,{0,Infinity}];
%t A124346 itrut[n_]:=itrut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[itrut/@c]]]/@IntegerPartitions[n-1],idthinQ]];
%t A124346 Table[Length[itrut[n]],{n,25}] (* _Gus Wiseman_, Jan 25 2018 *)
%Y A124346 Cf. A000081, A001678, A003238, A004111, A124343-A124348, A276625, A290689, A298303-A298305, A298422.
%Y A124346 Row sums of A245120.
%K A124346 nonn
%O A124346 1,4
%A A124346 _Christian G. Bower_, Oct 30 2006, suggested by _Franklin T. Adams-Watters_