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 A111998 #15 Mar 17 2017 21:59:14
%S A111998 1,10,75,500,3135,18962,112125,653200,3766950,21571500,122920642,
%T A111998 697994760,3953743250,22357130700,126273263510,712639689168,
%U A111998 4019975635855,22671014908550,127846248597125,720994336613980
%N A111998 Tenth convolution of Schroeder's (second problem) numbers A001003(n), n>=0.
%H A111998 Vincenzo Librandi, <a href="/A111998/b111998.txt">Table of n, a(n) for n = 0..300</a>
%F A111998 G.f.: ((1+x-sqrt(1-6*x+x^2))/(4*x))^10.
%F A111998 a(n) = (10/n)*Sum_{k=1,..,n} binomial(n,k)*binomial(n+k+9,k-1).
%F A111998 a(n) = 10*hypergeom([1-n, n+11], [2], -1), n>=1, a(0)=1.
%F A111998 Contribution from _Vaclav Kotesovec_, Oct 18 2012: (Start)
%F A111998 Recurrence: n*(n+10)*a(n) = (7*n^2+58*n+45)*a(n-1) - (7*n^2+40*n-18)*a(n-2) + (n-3)*(n+7)*a(n-3)
%F A111998 a(n) ~ 5*sqrt(3*sqrt(2)-4)*(1970-1393*sqrt(2)) * (3+2*sqrt(2))^(n+10)/(64*sqrt(Pi)*n^(3/2))
%F A111998 Generally, G.f. = ((1+x-sqrt(1-6*x+x^2))/(4*x))^k is asymptotic to a(n) ~ sqrt(3*sqrt(2)-4)*k*(1-1/sqrt(2))^(k-1) * (3+2*sqrt(2))^(n+k)/(4*sqrt(Pi)*n^(3/2)).
%F A111998 (End)
%t A111998 CoefficientList[Series[((1+x-Sqrt[1-6*x+x^2])/(4*x))^10, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 18 2012 *)
%o A111998 (PARI) x='x+O('x^50); Vec(((1+x-sqrt(1-6*x+x^2))/(4*x))^10) \\ _G. C. Greubel_, Mar 17 2017
%Y A111998 Cf. Tenth column of convolution triangle A011117.
%K A111998 nonn,easy
%O A111998 0,2
%A A111998 _Wolfdieter Lang_, Sep 12 2005