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 A339835 #8 Jan 09 2021 22:12:09
%S A339835 1,3,9,30,111,424,1705,7024,29692,127748,558219,2469403,11039992,
%T A339835 49796803,226348740,1035750855,4767429667,22058219466,102534463563,
%U A339835 478602668159,2242383155726,10541976883286,49714185649417,235109360767014,1114782699692044,5298494249055391
%N A339835 Number of rooted bicolored trees on n unlabeled nodes such that every white node is adjacent to a black node.
%H A339835 Andrew Howroyd, <a href="/A339835/b339835.txt">Table of n, a(n) for n = 1..500</a>
%e A339835 a(1) = 1: B.
%e A339835 a(2) = 4: B(B), B(W), W(B).
%e A339835 a(3) = 9: B(BB), B(BW), B(WW), W(BB), B(B(B)), B(B(W)), B(W(B)), W(B(B)), W(B(W)).
%o A339835 (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o A339835 seq(n)={my(u=v=w=[]); for(n=1, n, my(t1=EulerT(v), t2=EulerT(u+v)); u=concat([1], EulerT(u+v+w)); v=concat([0], t2-t1); w=concat([1], t1)); u+v}
%Y A339835 Cf. A038055 (rooted bicolored trees), A339831, A339834 (unrooted), A339838.
%K A339835 nonn
%O A339835 1,2
%A A339835 _Andrew Howroyd_, Dec 19 2020