A121011 Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/(5*8^2) = 1/320.

1, 320, 51200, 6553600, 5242880000, 1677721600000, 268435456000000, 343597383680000000, 2199023255552000000, 17592186044416000000000, 2814749767106560000000000, 1801439850948198400000000000

Offset

0,2

Comments

Numerators are given under A121010.

This is the third member (p=3) of the third p-family of partial sums of normalized scaled Catalan series CsnIII(p):=sum(((-1)^k)*C(k)/((5^k)*F(2*p)^(2*k)),k=0..infinity) with limit F(2*p)*(-L(2*p+1) + L(2*p)*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).

The partial sums of the above mentioned third p-family are rIII(p;n):=sum(((-1)^k)*C(k)/((5^k)*F(2*p)^(2*k)),k=0..n), n>=0, for p=1,...

For more details on this p-family and the other three ones see the W. Lang links under A120996 and A121010.

Links

Table of n, a(n) for n=0..11.

Formula

a(n)=denominator(r(n)) with r(n) := rIII(p=3,n) = sum(((-1)^k)*C(k)/((5^k)*F(2*3)^(2*k)),k=0..n), with F(6)=8 and C(k):=A000108(k) (Catalan). The rationals r(n) are given in lowest terms.

Example

Rationals r(n): [1, 319/320, 51041/51200, 6533247/6553600,
5226597607/5242880000, 1672511234219/1677721600000,...].

Crossrefs

The second member is A121008/A121009.

Sequence in context: A168636 A264140 A045813 * A264063 A174778 A300849

Adjacent sequences: A121008 A121009 A121010 * A121012 A121013 A121014

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Aug 16 2006

Status

approved