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 A349408 #18 Apr 14 2023 14:28:33
%S A349408 1,1,2,11,76,649,6173,63429,688898,7808246,91537482,1102931565,
%T A349408 13594564857,170804438005,2181426973452,28257128116954,
%U A349408 370581034530685,4913238656392058,65773613137623085,888155942037325535,12086555915234897267,165641209243876120135
%N A349408 Number of planar tanglegrams of size n.
%H A349408 Andrew Howroyd, <a href="/A349408/b349408.txt">Table of n, a(n) for n = 1..500</a>
%H A349408 Alexander E. Black, Kevin Liu, Alex Mcdonough, Garrett Nelson, Michael C. Wigal, Mei Yin, and Youngho Yoo, <a href="https://arxiv.org/abs/2304.05318">Sampling planar tanglegrams and pairs of disjoint triangulations</a>, arXiv:2304.05318 [math.CO], 2023.
%H A349408 Dimbinaina Ralaivaosaona, Jean Bernoulli Ravelomanana and Stephan Wagner, <a href="https://doi.org/10.4230/LIPIcs.AofA.2018.32">Counting Planar Tanglegrams</a>, LIPIcs Proceedings of Analysis of Algorithms 2018, Vol. 110. Article 32.
%F A349408 G.f.: F(x) satisfies F(x) = H(F(x)) + x + (F(x)^2 + F(x^2))/2 where H(x)/x^2 is the g.f. of A257887.
%e A349408 For n=4, there are 11 planar tanglegrams of size 4.
%o A349408 (PARI) \\ here H(n)/x^2 is g.f. of A257887.
%o A349408 H(n)={(x - x^2 - serreverse(sum(k=0, n+1, (binomial(2*k, k)/(k+1))^2*x^(k+1)) + O(x^(n+3))))/2}
%o A349408 seq(n)={my(h=H(n-2), p=O(x)); for(n=1, n, p = subst(h + O(x*x^n), x, p) + x + (p^2 + subst(p,x,x^2))/2); Vec(p)} \\ _Andrew Howroyd_, Nov 18 2021
%Y A349408 Row sums of A349409.
%Y A349408 Cf. A257887, A258620.
%K A349408 nonn
%O A349408 1,3
%A A349408 _Kevin Liu_, Nov 16 2021
%E A349408 Terms a(11) and beyond from _Andrew Howroyd_, Nov 18 2021