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 A351938 #5 Feb 26 2022 08:38:43
%S A351938 1,1,1,3,5,9,17,35,65,125,241,463,885,1701,3265,6271,12033,23105,
%T A351938 44353,85147,163445,313777,602353,1156339,2219809,4261389,8180561,
%U A351938 15704215,30147333,57873821,111100225,213278943,409431169,785984353,1508852673,2896541859
%N A351938 a(0) = 1; a(n) = -a(n-1) + 2 * Sum_{k=0..floor((n-1)/2)} a(k) * a(n-2*k-1).
%F A351938 G.f. A(x) satisfies: A(x) = 1 / (1 + x - 2 * x * A(x^2)).
%t A351938 a[0] = 1; a[n_] := a[n] = -a[n - 1] + 2 Sum[a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 35}]
%t A351938 nmax = 35; A[_] = 0; Do[A[x_] = 1/(1 + x - 2 x A[x^2]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A351938 Cf. A000621, A001003, A319436, A349365.
%K A351938 nonn
%O A351938 0,4
%A A351938 _Ilya Gutkovskiy_, Feb 26 2022