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 A349037 #5 Nov 06 2021 20:15:53
%S A349037 1,1,2,-1,29,116,7701,-103563,31343898,1759289595,2057705197793,
%T A349037 -457070362176172,2156748187140412361,1921405067209313680505,
%U A349037 36188075164863127910696914,-128870933294125665748520896793,9713904752944734908048841134573557
%N A349037 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(-4*x)).
%F A349037 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-2} (-4)^k * a(k) * a(n-k-2).
%t A349037 nmax = 16; A[_] = 0; Do[A[x_] = 1/(1 - x - x^2 A[-4 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A349037 a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[(-4)^k a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 16}]
%Y A349037 Cf. A001006, A015099, A348880, A349035, A349036.
%K A349037 sign
%O A349037 0,3
%A A349037 _Ilya Gutkovskiy_, Nov 06 2021