

A121499


Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/(29^2) = 1/841.


3



1, 841, 707281, 594823321, 500246412961, 420707233300201, 353814783205469041, 297558232675799463481, 250246473680347348787521, 210457284365172120330305161, 176994576151109753197786640401
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OFFSET

0,2


COMMENTS

Numerators are given under A121498.
This is the third member (p=3) of the fourth (normalized) pfamily 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).
The partial sums of the above mentioned fourth pfamily are rIV(p;n):=sum(((1)^k)*C(k)/L(2*p+1)^(2*k),k=0..n), n>=0, for p=1,...
For more details on this pfamily and the other three ones see the W. Lang links under A120996 and A121498.


LINKS

Table of n, a(n) for n=0..10.
Tanya Khovanova, Non Recursions


FORMULA

a(n)=denominator(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.


EXAMPLE

Rationals r(n): [1, 840/841, 706442/707281, 594117717/594823321,
499653000011/500246412961, 420208173009209/420707233300201,...].


CROSSREFS

The second member (p=2) of this pfamily is A121012/A121013.
Sequence in context: A108324 A133496 A253599 * A253514 A342841 A337730
Adjacent sequences: A121496 A121497 A121498 * A121500 A121501 A121502


KEYWORD

nonn,frac,easy


AUTHOR

Wolfdieter Lang, Aug 16 2006


STATUS

approved



