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 A380211 #21 Mar 22 2025 08:38:59 %S A380211 0,1,1,2,6,20,72,272,1064,4271,17497,72843,307307,1310792,5643555, %T A380211 24493270,107043258,470668034,2080681402,9242180923,41229189089, %U A380211 184634145428,829732117279,3740636883361,16912812764736,76673344515050,348449086540653,1587154540744158 %N A380211 Number of rooted binary normal unlabeled galled trees with n leaves. %C A380211 The asymptotic growth of a(n) follows (0.0779...)*(4.8230...^n)*n^(-3/2). %H A380211 Lily Agranat-Tamir, Shaili Mathur, and Noah A. Rosenberg, <a href="https://doi.org/10.1007/s11538-024-01270-8">Enumeration of rooted binary unlabeled galled trees</a>, Bull. Math. Biol. 86 (2024), 45. %F A380211 G.f. satisfies A(x) = 1 + x + (1/2)*A(x)^2 + (1/2)*A(x^2) - 1/(1-A(x)) + A(x)/(2*(1-A(x))^2) + A(x)/(2*(1-A(x^2))). %e A380211 For n=3 leaves, there is the unique rooted binary unlabeled tree with 3 leaves and no galls, and there is a rooted binary unlabeled tree with a root gall from which 3 leaves are descended; hence a(3)=2. %t A380211 terms = 28; A[_] = 0; Do[A[x_] = x + (1/2)*(A[x]^2 + A[x^2]) +A[x]((A[x]/(1-A[x]))^2+A[x^2]/(1-A[x^2]))/2+ O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Mar 22 2025 *) %Y A380211 Cf. A001190 (rooted binary unlabeled galled trees with n leaves and 0 galls). %K A380211 nonn %O A380211 0,4 %A A380211 _Noah A Rosenberg_, Jan 16 2025