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 A349032 #6 Nov 06 2021 20:15:19
%S A349032 1,2,0,-8,48,1024,-29376,-2008960,249483264,64889376256,
%T A349032 -32966832018432,-33890678261809152,69272943033878630400,
%U A349032 284019472607289480388608,-2325552273529676473281282048,-38111154065733485540332985155584,1248673879720871231428642700812025856
%N A349032 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(-2*x)).
%F A349032 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (-2)^k * a(k) * a(n-k-1).
%t A349032 nmax = 16; A[_] = 0; Do[A[x_] = 1/(1 - x - x A[-2 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A349032 a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[(-2)^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
%Y A349032 Cf. A006318, A015097, A348875, A349033, A349034.
%K A349032 sign
%O A349032 0,2
%A A349032 _Ilya Gutkovskiy_, Nov 06 2021