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%I #3 Mar 31 2012 13:20:12
%S 1,841,707281,594823321,500246412961,420707233300201,
%T 353814783205469041,297558232675799463481,250246473680347348787521,
%U 210457284365172120330305161,176994576151109753197786640401
%N Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/(29^2) = 1/841.
%C Numerators are given under A121498.
%C 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 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 For more details on this p-family and the other three ones see the W. Lang links under A120996 and A121498.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/NonRecursions.html">Non Recursions</a>
%F 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 Rationals r(n): [1, 840/841, 706442/707281, 594117717/594823321,
%e 499653000011/500246412961, 420208173009209/420707233300201,...].
%Y The second member (p=2) of this p-family is A121012/A121013.
%K nonn,frac,easy
%O 0,2
%A _Wolfdieter Lang_, Aug 16 2006
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