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 A355725 #4 Jul 18 2022 19:48:08
%S A355725 1,2,26,426,8178,176802,4206618,108577674,3011332338,89141101506,
%T A355725 2802596567706,93232011912426,3271729161905010,120810104634555234,
%U A355725 4683805718871051162,190294015841923438026,8087576641287426829170,358981130096398432055682,16615841072836741527510810
%N A355725 Row 5 of table A355721.
%H A355725 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 A355725 O.g.f: A(x) = ( Sum_{k >= 0} d(k+5)/d(5)*x^k )/( Sum_{k >= 0} d(k+4)/d(4)*x^k ), where d(n) = Product_{k = 1..n} (2*k-1) = A001147(n).
%F A355725 A(x) = 1/(1 + 9*x - 11*x/(1 + 11*x - 13*x/(1 + 13*x - 15*x/(1 + 15*x - ... )))).
%F A355725 The o.g.f. satisfies the Riccati differential equation 2*x^2*A'(x) + 9*x*A(x)^2 - (1 + 7*x)*A(x) + 1 = 0 with A(0) = 1.
%F A355725 Applying Stokes 1982 gives A(x) = 1/(1 - 2*x/(1 - 11*x/(1 - 4*x/(1 - 13*x/(1 - 6*x/(1 - 15*x/(1 - ... - 2*n*x/(1 - (2*n+9)*x )))))))), a continued fraction of Stieltjes-type.
%p A355725 n := 5: 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 A355725 Cf. A001147, A355721 (table), A112934 (row 0), A000698 (row 1), A355722 (row 2), A355723 (row 3), A355724 (row 4).
%K A355725 nonn,easy
%O A355725 0,2
%A A355725 _Peter Bala_, Jul 15 2022