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 A304914 #12 Oct 06 2019 01:50:43
%S A304914 1,1,2,4,9,21,55,146,415,1212,3653,11246,35346,112750,364714,1193202,
%T A304914 3943557,13148575,44186841,149536376,509270554,1744342614,6005869285,
%U A304914 20777091355,72192026878,251848377631,881865312582,3098564357293,10922162622233,38614641384893
%N A304914 Number of trees with positive integer edge labels summing to n.
%H A304914 Andrew Howroyd, <a href="/A304914/b304914.txt">Table of n, a(n) for n = 0..500</a>
%F A304914 G.f.: g(x) + (g(x^2) - g(x)^2)*x/(2*(1-x)) where g(x) is the g.f. of A052855.
%t A304914 max = 30; g[_] = 1; Do[g[x_] = Exp[Sum[(g[x^k]/(1 - x^k))*(x^k/k) + O[x]^n, {k, 1, n}]] // Normal, {n, 1, max}]; CoefficientList[g[x] + (g[x^2] - g[x]^2)*(x/(2*(1 - x))) + O[x]^max, x] (* _Jean-François Alcover_, May 25 2018 *)
%o A304914 (PARI) \\ here b(n) is A052855 as series
%o A304914 EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o A304914 b(n)={my(v=[1]); for(i=2, n, v=concat([1], v + EulerT(v))); Ser(v)*(1-x)}
%o A304914 seq(n)={my(g=b(n)); Vec(g + (subst(g,x,x^2) - g^2)*x/(2*(1-x)))}
%Y A304914 Row sums of A303842.
%Y A304914 Cf. A052855.
%K A304914 nonn
%O A304914 0,3
%A A304914 _Andrew Howroyd_, May 20 2018