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 A355722 #4 Jul 18 2022 19:47:36
%S A355722 1,2,14,138,1686,24162,394254,7191018,144786006,3188449602,
%T A355722 76246683534,1968284351178,54576250392726,1618348891438242,
%U A355722 51122453577462414,1714406473587300138,60843580566100937046,2278637898592632599682,89818339421620249242894,3717488491001699691500298
%N A355722 Row 2 of table A355721.
%H A355722 A. N. Stokes, <a href="https://doi.org/10.1017/S0004972700005219">Continued fraction solutions of the Riccati equation</a>, Bull. Austral. Math. Soc. Vol. 25 (1982), 207-214.
%F A355722 O.g.f: A(x) = ( Sum_{k >= 0} d(k+2)/d(2)*x^k )/( Sum_{k >= 0} d(k+1)/d(1)*x^k ), where d(n) = Product_{k = 1..n} (2*k-1) = A001147(n).
%F A355722 A(x)= 1/(1 + 3*x - 5*x/(1 + 5*x - 7*x/(1 + 7*x - 9*x/(1 + 9*x - ... )))).
%F A355722 The o.g.f. satisfies the Riccati differential equation 2*x^2*A'(x) + 3*x*A(x)^2 - (1 + x)*A(x) + 1 = 0 with A(0) = 1.
%F A355722 Applying Stokes 1982 gives A(x) = 1/(1 - 2*x/(1 - 5*x/(1 - 4*x/(1 - 7*x/(1 - 6*x/(1 - 9*x/(1 - ... - 2*n*x/(1 - (2*n+3)*x )))))))), a continued fraction of Stieltjes type.
%p A355722 n := 2: seq(coeff(series( hypergeom([n+1/2, 1], [], 2*x)/hypergeom([n-1/2, 1], [], 2*x ), x, 21), x, k), k = 0..20);
%Y A355722 Cf. A001147, A355721 (table), A112934 (row 0), A000698 (row 1), A355723 (row 3), A355724 (row 4), A355725 (row 5).
%K A355722 nonn,easy
%O A355722 0,2
%A A355722 _Peter Bala_, Jul 15 2022