%I A121498
%S A121498 1,840,706442,594117717,499653000011,420208173009209,353395073500744901,
%T A121498 297205256814126461312,249949620980680353964822,
%U A121498 210207631244752177684410440,176784617876836581432589196836
%N A121498 Numerators of partial alternating sums of Catalan numbers scaled by powers 
               of 1/(29^2) = 1/841.
%C A121498 Denominators are given under A121499.
%C A121498 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 A121498 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 A121498 For more details on this p-family and the other three ones see the W. 
               Lang link under A120996.
%H A121498 W. Lang: <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A121498.text">
               Rationals r(n), limit.</a>
%F A121498 a(n)=numerator(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 A121498 Rationals r(n): [1, 840/841, 706442/707281, 594117717/594823321,
%e A121498 499653000011/500246412961, 420208173009209/420707233300201,...].
%p A121498 The limit lim_{n->infinity}(r(n) := rIV(2;n)) = 29*(-21 + 13*phi) = 29/
               phi^7 = 0.998813758709 (maple10, 10 digits).
%Y A121498 The second member (p=2) of this p-family is A121012/A121013.
%Y A121498 Sequence in context: A091035 A091036 A091038 this_sequence A159690 A108324 
               A133496
%Y A121498 Adjacent sequences: A121495 A121496 A121497 this_sequence A121499 A121500 
               A121501
%K A121498 nonn,frac,easy
%O A121498 0,2
%A A121498 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 16 
               2006