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 A352865 #5 Apr 07 2022 09:25:16
%S A352865 1,1,1,-1,-4,-5,6,36,46,-101,-515,-506,2554,9991,3067,-79915,-227056,
%T A352865 205681,2841708,5134140,-18296153,-107927240,-66578269,1174691649,
%U A352865 4059143386,-4667894370,-69377504739,-126787267800,669710503012,3835079736835,475781902203
%N A352865 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n-k,k) * a(n-2*k-1).
%F A352865 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 + x^2)) / (1 + x^2)^2.
%t A352865 a[0] = 1; a[n_] := a[n] = Sum[(-1)^k Binomial[n - k, k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 30}]
%t A352865 nmax = 30; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 + x^2)]/(1 + x^2)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]
%Y A352865 Cf. A014619, A172385, A352864.
%K A352865 sign
%O A352865 0,5
%A A352865 _Ilya Gutkovskiy_, Apr 06 2022