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 A088352 #19 Dec 05 2019 16:12:08
%S A088352 1,1,2,3,5,9,16,28,50,89,158,282,503,896,1598,2850,5082,9064,16166,
%T A088352 28832,51424,91719,163588,291774,520407,928196,1655530,2952805,
%U A088352 5266626,9393565,16754386,29883166,53299700,95065503,169559118,302426167,539408258,962090267
%N A088352 G.f. = continued fraction: A(x) = 1/(1-x-x^2/(1-x^3-x^4/(1-x^5-x^6/(1-x^7-x^8/(...))))).
%C A088352 From _Peter Bala_, Jul 29 2019: (Start)
%C A088352 a(n) = the number of triangle stacks of large Schröder type on n triangles. See Links for a definition and an illustration.
%C A088352 Cf. A224704, which enumerates triangle stacks (of small Schröder type) on n triangles and A143951, which enumerates triangle stacks (of Dyck type) on n triangles. (End)
%H A088352 Vaclav Kotesovec, <a href="/A088352/b088352.txt">Table of n, a(n) for n = 0..300</a>
%H A088352 P. Bala, <a href="/A088352/a088352.pdf">Illustration for a(5) = 9</a>
%F A088352 a(n) ~ c * d^n, where d = 1.78360320457574331710673100097614660803225788206... and c = 0.4843739369092187339166963460525819972933890792971... - _Vaclav Kotesovec_, Jul 01 2019
%F A088352 From _Peter Bala_, Jul 29 2019: (Start)
%F A088352 O.g.f. as a continued fraction: A(q) = 1/(1 - q*(1 + q)/(1 - q^4/(1 - q^3*(1 + q^3)/(1 - q^8/( 1 - q^5*(1 + q^5)/(1 - q^12/( (...) ))))))).
%F A088352 O.g.f. as a ratio of q-series: A(q) = N(q)/D(q), where N(q) = Sum_{n >= 0} (-1)^n*q^(2*n^2+2*n)/( Product_{k = 1..2*n+1} (1 - q^k) ) and D(q) = Sum_{n >= 0} (-1)^n*q^(2*n^2)/( Product_{k = 1..2*n} (1 - q^k) ).
%F A088352 In the above asymptotic formula, 1/d = 0.5606628186... is the minimal positive real zero of D(q), and is the dominant singularity of N(q)/D(q). (End)
%t A088352 nmax = 40; CoefficientList[Series[1/(1 - x + ContinuedFractionK[-x^(2*k), 1 - x^(2*k + 1), {k, 1, nmax}]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 01 2019 *)
%Y A088352 Cf. A143951, A224704.
%K A088352 nonn,easy
%O A088352 0,3
%A A088352 _Paul D. Hanna_, Sep 26 2003
%E A088352 More terms from _Vaclav Kotesovec_, Jul 01 2019