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 A349033 #6 Nov 06 2021 20:15:28
%S A349033 1,2,-2,-34,826,70634,-16895162,-12385295242,27037369868722,
%T A349033 177500531682526034,-3493033395457140741746,
%U A349033 -206274103942288894158940594,36540013650535335202759969693162,19419007557809179132528500713950083002,-30960092711143410415029705970483650552421802
%N A349033 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(-3*x)).
%F A349033 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (-3)^k * a(k) * a(n-k-1).
%t A349033 nmax = 14; A[_] = 0; Do[A[x_] = 1/(1 - x - x A[-3 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A349033 a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[(-3)^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 14}]
%Y A349033 Cf. A006318, A015098, A348876, A349032, A349034.
%K A349033 sign
%O A349033 0,2
%A A349033 _Ilya Gutkovskiy_, Nov 06 2021