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 A371659 #14 Apr 28 2024 11:21:36 %S A371659 1,0,1,0,1,1,0,3,3,5,0,13,9,20,34,0,90,46,70,170,273,0,747,312,360, %T A371659 680,1638,2436,0,7040,2580,2435,3570,7371,17052,23391,0,71736,24056, %U A371659 19800,23970,39858,85260,187128,237090,0,774738,243483,182850,193664,267813,477456,1029204,2133810,2505228 %N A371659 Triangle read by rows: T(n,k) is the number of planar tanglegrams of size n with irreducible component of size k. %C A371659 A proper subtanglegram of a planar tanglegram is a pair of subtrees whose leaves are matched in the tanglegram, and the irreducible component of a planar tanglegram is formed by contracting each maximal proper subtanglegram into a pair of matched leaves. %H A371659 Alexander E. Black, Kevin Liu, Alex McDonough, Garrett Nelson, Michael C. Wigal, Mei Yin, and Youngho Yoo, <a href="https://doi.org/10.1016/j.aam.2023.102550">Sampling planar tanglegrams and pairs of disjoint triangulations</a>, Advances in Applied Mathematics 149 (2023), Paper No. 102550. %F A371659 G.f.: F(x,y) = H(F(x),y) + x*y + y^2*(F(x)^2 + F(x^2))/2 where the coefficient of x^n*y^k is the number of planar tanglegrams of size n with irreducible component of size k, F(x) is the g.f. for A349408, and H(x)/x^2 is the g.f. for A257887. %e A371659 Triangle begins %e A371659 1; %e A371659 0, 1; %e A371659 0, 1, 1; %e A371659 0, 3, 3, 5; %e A371659 0, 13, 9, 20, 34; %e A371659 0, 90, 46, 70, 170, 273; %e A371659 0, 747, 312, 360, 680, 1638, 2436; %e A371659 0, 7040, 2580, 2435, 3570, 7371, 17052, 23391; %e A371659 ... %Y A371659 Cf. A349408 (diagonal), A257887 (row sums). %K A371659 nonn,tabl %O A371659 1,8 %A A371659 _Kevin Liu_, Apr 01 2024