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 A068771 #18 Feb 03 2025 09:36:52
%S A068771 1,1,18,333,6318,122634,2429028,48974949,1002875094,20814628158,
%T A068771 437088964860,9272342710962,198456435657036,4280758166952756,
%U A068771 92972201833888200,2031520673763657621,44630859892110807654
%N A068771 Generalized Catalan numbers 9*x*A(x)^2 -A(x) +1 -8*x=0.
%H A068771 Fung Lam, <a href="/A068771/b068771.txt">Table of n, a(n) for n = 0..725</a>
%F A068771 a(n) = (9^n) * p(n, -8/9) with the row polynomials p(n, x) defined from array A068763.
%F A068771 a(n+1) = 9*sum(a(k)*a(n-k), k=0..n), n>=1, a(0)=1=a(1).
%F A068771 G.f.: (1-sqrt(1-36*x*(1-8*x)))/(18*x).
%F A068771 Recurrence: (n+1)*a(n) = 288*(2-n)*a(n-2) + 18*(2*n-1)*a(n-1). - _Fung Lam_, Mar 04 2014
%F A068771 a(n) ~ sqrt(2) * 24^n / (3*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Mar 04 2014
%t A068771 a[n_] := (288 (2 - n) a[n - 2] + 18 (2 n - 1) a[n - 1])/(n + 1); Table[a[n], {n, 0, 20}](* _Wesley Ivan Hurt_, Mar 04 2014 *)
%t A068771 CoefficientList[Series[(1-Sqrt[1-36*x*(1-8*x)])/(18*x), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 04 2014 *)
%Y A068771 Cf. A000108, A068764-A068770, A068772, A025227-A025230.
%K A068771 nonn,easy
%O A068771 0,3
%A A068771 _Wolfdieter Lang_, Mar 04 2002