Search: id:A121013
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%I A121013
%S A121013 1,121,14641,1771561,214358881,25937424601,285311670611,34522712143931,
%T A121013 4177248169415651,505447028499293771,672749994932560009201,
%U A121013 81402749386839761113321,9849732675807611094711841
%N A121013 Denominators of partial alternating sums of Catalan numbers scaled by 
               powers of 1/(11^2) = 1/121.
%C A121013 This is the second member (p=2) of the fourth (normalized) p-family of 
               partial sums of the 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), where C(n)=A000108(n) (Catalan), F(n)= A000045(n) 
               (Fibonacci), L(n) = A000032(n) (Lucas) and phi:=(1+sqrt(5))/2 (golden 
               section).
%C A121013 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 A121013 For more details on this p-family and the other three ones see the W. 
               Lang links under A120996 and A121012.
%F A121013 a(n)=denominator(r(n)) with r(n) := rIV(p=2,n) = sum(((-1)^k)*C(k)/L(2*2+1)^(2*k), 
               k=0..n), with L(5)=11 and C(k):=A000108(k) (Catalan). The rationals 
               r(n) are given in lowest terms.
%e A121013 Rationals r(n): [1, 120/121, 14522/14641, 1757157/1771561, 212616011/
               214358881, 25726537289/25937424601,...].
%Y A121013 The first member is A120794/A120785. The third member is A121498/A121499.
%Y A121013 Sequence in context: A066625 A078277 A050740 this_sequence A129450 A082489 
               A028463
%Y A121013 Adjacent sequences: A121010 A121011 A121012 this_sequence A121014 A121015 
               A121016
%K A121013 nonn,frac,easy
%O A121013 0,2
%A A121013 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 16 
               2006

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