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 A111997 #14 Mar 17 2017 00:47:38
%S A111997 1,9,63,399,2403,14067,80949,460845,2605590,14666470,82320714,
%T A111997 461238282,2581644378,14442658074,80785970838,451934259654,
%U A111997 2528977211775,14157983986839,79302044283297,444448115168049,2492468172937125
%N A111997 Ninth convolution of Schroeder's (second problem) numbers A001003(n), n>=0.
%H A111997 Vincenzo Librandi, <a href="/A111997/b111997.txt">Table of n, a(n) for n = 0..200</a>
%F A111997 G.f.: ((1+x-sqrt(1-6*x+x^2))/(4*x))^9.
%F A111997 a(n) = (9/n)*Sum_{k=1,..,n} binomial(n,k)*binomial(n+k+8,k-1).
%F A111997 a(n) = 9*hypergeom([1-n, n+10], [2], -1), n>=1, a(0)=1.
%F A111997 Recurrence: n*(n+9)*a(n) = (7*n^2+51*n+32)*a(n-1) - (7*n^2+33*n-22)*a(n-2) + (n-3)*(n+6)*a(n-3). - _Vaclav Kotesovec_, Oct 18 2012
%F A111997 a(n) ~ 9*sqrt(3*sqrt(2)-4)*(577-408*sqrt(2)) * (3+2*sqrt(2))^(n+9)/(64*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 18 2012
%t A111997 CoefficientList[Series[((1+x-Sqrt[1-6*x+x^2])/(4*x))^9, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 18 2012 *)
%o A111997 (PARI) x='x+O('x^50); Vec(((1+x-sqrt(1-6*x+x^2))/(4*x))^9) \\ _G. C. Greubel_, Mar 17 2017
%Y A111997 Ninth column of convolution triangle A011117.
%K A111997 nonn,easy
%O A111997 0,2
%A A111997 _Wolfdieter Lang_, Sep 12 2005