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 A349286 #7 Nov 13 2021 12:43:52
%S A349286 1,1,7,148,8695,1455433,715092412,1046279830240,4581706851060703,
%T A349286 60144130721142806611,2367934845363738749478583,
%U A349286 279660212608573899258160179472,99083333806943049370375436233999876,105314387436569180750449877597844106742044
%N A349286 G.f. A(x) satisfies: A(x) = 1 / (1 - x * A(3*x)^2).
%F A349286 a(0) = 1; a(n) = Sum_{i=0..n-1} Sum_{j=0..n-i-1} 3^(i+j) * a(i) * a(j) * a(n-i-j-1).
%F A349286 a(n) ~ c * 3^(n*(n-1)/2) * 2^n, where c = 0.7827821536020754599551185976017878354967268590673601224489106938395... - _Vaclav Kotesovec_, Nov 13 2021
%t A349286 nmax = 13; A[_] = 0; Do[A[x_] = 1/(1 - x A[3 x]^2) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A349286 a[0] = 1; a[n_] := a[n] = Sum[Sum[3^(i + j) a[i] a[j] a[n - i - j - 1], {j, 0, n - i - 1}], {i, 0, n - 1}]; Table[a[n], {n, 0, 13}]
%Y A349286 Cf. A001764, A015084, A171192, A349287.
%K A349286 nonn
%O A349286 0,3
%A A349286 _Ilya Gutkovskiy_, Nov 13 2021