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 A348878 #9 Nov 03 2021 05:19:26
%S A348878 1,1,2,5,17,74,429,3297,34578,495573,9888497,274123802,10685538941,
%T A348878 583079000129,44945515778914,4867082587900837,746167748281132753,
%U A348878 160981861948404281578,49223569713040994430285,21198824279482430844823713,12946110661470835825027893426
%N A348878 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(2*x)).
%F A348878 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-2} 2^k * a(k) * a(n-k-2).
%F A348878 a(n) ~ c * 2^(n*(n-2)/4), where c = 10.492153305884170498003413429333844276557493974205102819840538218355... - _Vaclav Kotesovec_, Nov 03 2021
%t A348878 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 A348878 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 A348878 Cf. A001006, A015083, A348879, A348880.
%K A348878 nonn
%O A348878 0,3
%A A348878 _Ilya Gutkovskiy_, Nov 02 2021