A121005 - OEIS

%I #5 Mar 31 2012 13:20:12

%S 1,125,15625,390625,244140625,30517578125,3814697265625,

%T 476837158203125,11920928955078125,7450580596923828125,

%U 931322574615478515625,116415321826934814453125,14551915228366851806640625

%N Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/125.

%C This is the third member (p=2) of the second p-family of partial sums of normalized scaled Catalan series CsnII(p):=sum(C(k)/((5^k)*F(2*p+1)^(2*k)),k=0..infinity) with limit F(2*p+1)*(L(2*p+2) - L(2*p+1)*phi) = F(2*p)*sqrt(5)/phi^(2*p), 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 second p-family are rII(p;n):=sum(C(k)/((5^k)*F(2*p+1)^(2*k)),k=0..n), n>=0, for p=0,1,...

%C For more details on this p-family and the other three ones see the W. Lang link under A120996.

%C Numerators are given under A121004.

%F a(n)=denominator(r(n)) with r(n) := rII(p=2,n) = sum(C(k)/5^(3*k),k=0..n) and C(k):=A000108(k) (Catalan). The rationals r(n) are given in lowest terms.

%e Rationals r(n): [1, 126/125, 15752/15625, 393801/390625,

%e 246125639/244140625, 30765704917/30517578125,...].

%K nonn,frac,easy

%O 0,2

%A _Wolfdieter Lang_, Aug 16 2006