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 A298533 #9 May 21 2018 15:09:25
%S A298533 1,1,2,4,8,15,31,64,144,333,808,2004,5109,13199,34601,91539,244307,
%T A298533 656346,1774212,4820356,13157591,36060811,99198470,273790194,
%U A298533 757971757,2104222594,5856496542,16338140048,45678276507,127964625782,359155302204,1009790944307
%N A298533 Number of unlabeled rooted trees with n vertices such that every branch of the root has the same number of leaves.
%H A298533 Andrew Howroyd, <a href="/A298533/b298533.txt">Table of n, a(n) for n = 1..500</a>
%e A298533 The a(5) = 8 trees: ((((o)))), (((oo))), ((o(o))), ((ooo)), (o((o))), ((o)(o)), (oo(o)), (oooo)
%t A298533 rut[n_]:=rut[n]=If[n===1,{{}},Join@@Function[c,Union[Sort/@Tuples[rut/@c]]]/@IntegerPartitions[n-1]];
%t A298533 Table[Length[Select[rut[n],SameQ@@(Count[#,{},{0,Infinity}]&/@#)&]],{n,15}]
%o A298533 (PARI) \\ here R is A055277 as vector of polynomials
%o A298533 EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o A298533 R(n) = {my(A = O(x)); for(j=1, n, A = x*(y - 1 + exp( sum(i=1, j, 1/i * subst( subst( A + x * O(x^(j\i)), x, x^i), y, y^i) ) ))); Vec(A)};
%o A298533 seq(n)={my(M=Mat(apply(p->Colrev(p,n), R(n-1)))); concat([1],sum(i=2, #M, EulerT(M[i,])))} \\ _Andrew Howroyd_, May 20 2018
%Y A298533 Cf. A000081, A003238, A004111, A032305, A289079, A290689, A291443, A297791, A298422, A298534, A298535.
%K A298533 nonn
%O A298533 1,3
%A A298533 _Gus Wiseman_, Jan 20 2018
%E A298533 Terms a(19) and beyond from _Andrew Howroyd_, May 20 2018