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 A349035 #6 Nov 06 2021 20:15:40
%S A349035 1,1,2,1,9,6,165,97,10970,8617,2838793,1206206,2912348749,3338391105,
%T A349035 11938619074866,-3485058191151,195607339607544393,505337929567029942,
%U A349035 12820529140255160177781,-40595263531274884237983,3360756421633193695872693450
%N A349035 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(-2*x)).
%F A349035 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-2} (-2)^k * a(k) * a(n-k-2).
%t A349035 nmax = 20; A[_] = 0; Do[A[x_] = 1/(1 - x - x^2 A[-2 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A349035 a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[(-2)^k a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 20}]
%Y A349035 Cf. A001006, A015097, A348878, A349036, A349037.
%K A349035 sign
%O A349035 0,3
%A A349035 _Ilya Gutkovskiy_, Nov 06 2021