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 A068768 #21 Feb 03 2025 09:36:38
%S A068768 1,1,12,150,1944,25992,356832,5008824,71629920,1040509152,15315578496,
%T A068768 227981324736,3426473187072,51929043390720,792725911280640,
%U A068768 12178706839758720,188158789025809920,2921622674591946240
%N A068768 Generalized Catalan numbers 6*x*A(x)^2 -A(x) +1 -5*x =0.
%C A068768 a(n) = K(6,6; n)/6 with K(a,b; n) defined in a comment to A068763.
%H A068768 Fung Lam, <a href="/A068768/b068768.txt">Table of n, a(n) for n = 0..810</a>
%F A068768 a(n) = (6^n) * p(n, -5/6) with the row polynomials p(n, x) defined from array A068763.
%F A068768 a(n+1) = 6*sum(a(k)*a(n-k), k=0..n), n>=1, a(0)=1=a(1).
%F A068768 G.f.: (1-sqrt(1-24*x*(1-5*x)))/(12*x).
%F A068768 D-finite with recurrence: (n+1)*a(n) = 120*(2-n)*a(n-2) + 12*(2*n-1)*a(n-1). - _Fung Lam_, Mar 04 2014
%F A068768 a(n) ~ sqrt(3+3*sqrt(6)) * (12+2*sqrt(6))^n / (6*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Mar 04 2014
%t A068768 CoefficientList[Series[(1-Sqrt[1-24*x*(1-5*x)])/(12*x), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 04 2014 *)
%Y A068768 Cf. A000108, A068764-A068767, A068769-A068772, A025227-A025230.
%K A068768 nonn,easy
%O A068768 0,3
%A A068768 _Wolfdieter Lang_, Mar 04 2002