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 A307489 #9 Sep 16 2021 13:32:23
%S A307489 1,3,19,152,1367,13195,133556,1398696,15029311,164764985,1835614027,
%T A307489 20722066612,236524088612,2725081792932,31649837891768,
%U A307489 370161223462480,4355751419996559,51532214460643957,612604251998847641,7313900470316335280,87659840436181657215
%N A307489 G.f. A(x) satisfies: A(x) = 1/(1 - 2*x*A(x) - x*A(x)/(1 - x*A(x)/(1 - x*A(x)/(1 - ...)))), a continued fraction.
%F A307489 G.f. A(x) satisfies: A(x) = 2/(1 - 4*x*A(x) + sqrt(1 - 4*x*A(x))).
%F A307489 G.f. A(x) satisfies: A(x) = Sum_{k>=0} binomial(2*k+1,k+1)*x^k*A(x)^k.
%F A307489 G.f.: A(x) = (1/x)*Series_Reversion(x*(1 - 4*x + sqrt(1 - 4*x))/2).
%F A307489 a(n) ~ 2^(12*n + 5) / (sqrt(Pi) * 17^(1/4) * n^(3/2) * (107 + 51*sqrt(17))^(n + 1/2)). - _Vaclav Kotesovec_, Sep 16 2021
%e A307489 G.f.: A(x) = 1 + 3*x + 19*x^2 + 152*x^3 + 1367*x^4 + 13195*x^5 + 133556*x^6 + 1398696*x^7 + 15029311*x^8 + 164764985*x^9 + 1835614027*x^10 + ...
%t A307489 terms = 21; CoefficientList[1/x InverseSeries[Series[x (1 - 4 x + Sqrt[1 - 4 x])/2, {x, 0, terms}], x], x]
%t A307489 terms = 21; A[_] = 0; Do[A[x_] = 1/(1 - 2 x A[x] + ContinuedFractionK[-x A[x], 1, {k, 1, j}]) + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
%t A307489 terms = 20; A[_] = 1; Do[A[x_] = 2/(1 - 4 x A[x] + Sqrt[1 - 4 x A[x]]) + O[x]^(terms + 1) // Normal, {terms + 1}]; CoefficientList[A[x], x]
%t A307489 terms = 21; A[_] = 1; Do[A[x_] = Sum[Binomial[2 k + 1, k + 1] x^k A[x]^k, {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
%Y A307489 Cf. A001700, A001764, A078531, A246432, A307490.
%K A307489 nonn
%O A307489 0,2
%A A307489 _Ilya Gutkovskiy_, Apr 10 2019