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 A121499 #3 Mar 31 2012 13:20:12 %S A121499 1,841,707281,594823321,500246412961,420707233300201, %T A121499 353814783205469041,297558232675799463481,250246473680347348787521, %U A121499 210457284365172120330305161,176994576151109753197786640401 %N A121499 Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/(29^2) = 1/841. %C A121499 Numerators are given under A121498. %C A121499 This is the third member (p=3) of the fourth (normalized) p-family of partial sums of normalized scaled Catalan series CsnIV(p):=sum(((-1)^k)*C(k)/L(2*p+1)^(2*k),k=0..infinity) with limit L(2*p+1)*(-F(2*p+2) + F(2*p+1)*phi) = L(2*p+1)/phi^(2*p+1), with C(n)=A000108(n) (Catalan), F(n)= A000045(n) (Fibonacci), L(n) = A000032(n) (Lucas) and phi:=(1+sqrt(5))/2 (golden section). %C A121499 The partial sums of the above mentioned fourth p-family are rIV(p;n):=sum(((-1)^k)*C(k)/L(2*p+1)^(2*k),k=0..n), n>=0, for p=1,... %C A121499 For more details on this p-family and the other three ones see the W. Lang links under A120996 and A121498. %H A121499 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/NonRecursions.html">Non Recursions</a> %F A121499 a(n)=denominator(r(n)) with r(n) := rIV(p=3,n) = sum(((-1)^k)*C(k)/L(2*3+1)^(2*k),k=0..n), with L(7)=29 and C(k):=A000108(k) (Catalan). The rationals r(n) are given in lowest terms. %e A121499 Rationals r(n): [1, 840/841, 706442/707281, 594117717/594823321, %e A121499 499653000011/500246412961, 420208173009209/420707233300201,...]. %Y A121499 The second member (p=2) of this p-family is A121012/A121013. %K A121499 nonn,frac,easy %O A121499 0,2 %A A121499 _Wolfdieter Lang_, Aug 16 2006