%I A121499
%S A121499 1,841,707281,594823321,500246412961,420707233300201,353814783205469041,
%T A121499 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.
%Y A121499 Sequence in context: A159690 A108324 A133496 this_sequence A049530 A158404 
               A004929
%Y A121499 Adjacent sequences: A121496 A121497 A121498 this_sequence A121500 A121501 
               A121502
%K A121499 nonn,frac,easy
%O A121499 0,2
%A A121499 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 16 
               2006