

A120999


Denominators of partial sums of Catalan numbers scaled by powers of 1/7^2 = 1/49.


1



1, 49, 2401, 117649, 823543, 40353607, 13841287201, 678223072849, 33232930569601, 1628413597910449, 79792266297612001, 558545864083284007, 27368747340080916343, 9387480337647754305649, 459986536544739960976801
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OFFSET

0,2


COMMENTS

Numerators are given under A120998.
This is the third member (p=2) of the first pfamily of partial sums of normalized scaled Catalan series CsnI(p):=sum(C(k)/L(2*p)^(2*k),k=0..infinity) with limit L(2*p)*(F(2*p+1)  F(2*p)*phi) = L(2*p)/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).
See A120998 for more details and a W. Lang link there for the definition of four pfamilies of such scaled Catalan sums.


LINKS

Table of n, a(n) for n=0..14.


FORMULA

a(n)=denominator(r(n)) with r(n) := rI(p=2,n) = sum(C(k)/L(4)^(2*k),k=0..n), with Lucas L(4)=7 and C(k):=A000108(k) (Catalan). The rationals r(n) are given in lowest terms.


EXAMPLE

Rationals r(n): [1, 50/49, 2452/2401, 120153/117649, 841073/823543,
41212583/40353607, 14135916101/13841287201,...].


CROSSREFS

Sequence in context: A170730 A170768 A218751 * A087752 A069741 A203384
Adjacent sequences: A120996 A120997 A120998 * A121000 A121001 A121002


KEYWORD

nonn,frac,easy


AUTHOR

Wolfdieter Lang, Aug 16 2006


STATUS

approved



