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 A365696 #11 Sep 26 2023 05:27:46
%S A365696 1,0,0,0,1,1,1,1,3,6,10,15,26,49,92,165,294,535,994,1852,3437,6379,
%T A365696 11905,22344,42058,79260,149601,283038,536806,1020066,1941317,3699922,
%U A365696 7062308,13500402,25842489,49528164,95031920,182545222,351023451,675678911,1301838177
%N A365696 G.f. satisfies A(x) = 1 + x^4*A(x)^2 / (1 - x*A(x)).
%F A365696 a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k-1,n-4*k) * binomial(n-2*k+1,k) / (n-2*k+1).
%F A365696 From _Vaclav Kotesovec_, Sep 26 2023: (Start)
%F A365696 G.f.: (1 + x - sqrt(1 - 2*x + x^2 - 4*x^4)) / (2*x*(1 + x^3)).
%F A365696 a(n) ~ 2^(n + 3/2) / (sqrt(Pi) * 3^(3/2) * n^(3/2)). (End)
%t A365696 CoefficientList[Series[(1 + x - Sqrt[1 - 2*x + x^2 - 4*x^4])/(2*x*(1 + x^3)), {x, 0, 40}], x] (* _Vaclav Kotesovec_, Sep 26 2023 *)
%o A365696 (PARI) a(n) = sum(k=0, n\4, binomial(n-3*k-1, n-4*k)*binomial(n-2*k+1, k)/(n-2*k+1));
%Y A365696 Cf. A023427, A215341, A215342, A357308, A365697.
%Y A365696 Cf. A112805.
%K A365696 nonn
%O A365696 0,9
%A A365696 _Seiichi Manyama_, Sep 16 2023