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 A298539 #8 Jan 29 2018 07:57:34
%S A298539 1,1,1,3,6,15,35,89,218,571,1446,3834,10003,26864,71120,193602,519409,
%T A298539 1423539,3865590,10666555,29185905,81078369,223367624,623192655,
%U A298539 1727907182,4840616872,13482957335,37923616139,106070402639,299214369115,840217034149
%N A298539 Number of unlabeled rooted trees with n vertices such that every branch of the root has a different number of nodes.
%H A298539 Alois P. Heinz, <a href="/A298539/b298539.txt">Table of n, a(n) for n = 1..1000</a>
%F A298539 G.f.: Product_{n>0} (1 + A000081(n) x^n).
%e A298539 The a(5) = 6 trees: ((((o)))), (((oo))), ((o(o))), ((ooo)), (o((o))), (o(oo)).
%t A298539 nn=20;
%t A298539 r[n_]:=r[n]=If[n===1,1,Sum[Product[Binomial[r[x]+Count[ptn,x]-1,Count[ptn,x]],{x,Union[ptn]}],{ptn,IntegerPartitions[n-1]}]];
%t A298539 Table[SeriesCoefficient[Product[1+r[n]x^n,{n,nn}],{x,0,n}],{n,0,nn}]
%Y A298539 Cf. A000081, A004111, A032305, A290689, A298422, A298533, A298535, A298537, A298539.
%K A298539 nonn
%O A298539 1,4
%A A298539 _Gus Wiseman_, Jan 21 2018