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 A364625 #9 Jul 30 2023 09:56:39
%S A364625 1,3,7,16,38,95,249,678,1901,5451,15906,47066,140868,425657,1296665,
%T A364625 3977684,12276617,38094013,118768915,371875752,1168843808,3686549845,
%U A364625 11664123048,37011249678,117750111763,375529083267,1200327617200,3844662925222,12338289374046
%N A364625 G.f. satisfies A(x) = 1/(1-x)^3 + x^2*A(x)^2.
%F A364625 G.f.: A(x) = 2 / ( (1-x)^3 * (1 + sqrt( 1 - 4*x^2/(1-x)^3 )) ).
%F A364625 a(n) = Sum_{k=0..floor(n/2)} binomial(n+k+2,3*k+2) * binomial(2*k,k) / (k+1).
%o A364625 (PARI) my(N=30, x='x+O('x^N)); Vec(2/((1-x)^3*(1+sqrt(1-4*x^2/(1-x)^3))))
%Y A364625 Cf. A000108, A086615, A162481, A360045.
%Y A364625 Cf. A364626, A364627.
%K A364625 nonn
%O A364625 0,2
%A A364625 _Seiichi Manyama_, Jul 30 2023