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A121003 Denominators of partial sums of Catalan numbers scaled by powers of 1/5. 1


%S 1,5,25,25,625,3125,15625,78125,3125,1953125,9765625,48828125,

%T 244140625,244140625,1220703125,6103515625,30517578125,152587890625,

%U 152587890625,3814697265625,19073486328125

%N Denominators of partial sums of Catalan numbers scaled by powers of 1/5.

%C Numerators are given under A121002.

%C This is the first member (p=0) 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+1)*sqrt(5)/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 For more details on this p-family and the other three ones see the W. Lang links under A120996 and A121002.

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

%e Rationals r(n): [1, 6/5, 32/25, 33/25, 839/625, 4237/3125,

%e 21317/15625, 107014/78125, 4292/3125, 2687362/1953125,...].

%e A120787 (denominators, second member p=1).

%K nonn,frac,easy

%O 0,2

%A _Wolfdieter Lang_, Aug 16 2006

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