|
Search: id:A121001
|
|
|
| A121001 |
|
Denominators of partial sums of Catalan numbers scaled by powers of 1/18^2 = 1/324. |
|
+0
2
|
|
| 1, 324, 52488, 34012224, 5509980288, 595077871104, 96402615118848, 124937789194027008, 60719765548297125888, 19673204037648268787712, 3187059054099019543609344, 2065214267056164664258854912
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Numerators are given under A121000.
This is the fourth member (p=3) of the first p-family 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 p-families of such scaled Catalan sums.
|
|
FORMULA
|
a(n)=denominator(r(n)) with r(n) := rI(p=3,n) = sum(C(k)/L(6)^(2*k),k=0..n), with Lucas L(6)=18, and C(k):=A000108(k) (Catalan). The rationals r(n) are given in lowest terms.
|
|
EXAMPLE
|
Rationals r(n): [1, 325/324, 52651/52488, 34117853/34012224, 5527092193/5509980288, 596925956851/595077871104, ...].
|
|
CROSSREFS
|
Sequence in context: A128381 A128992 A088216 this_sequence A132644 A013763 A013887
Adjacent sequences: A120998 A120999 A121000 this_sequence A121002 A121003 A121004
|
|
KEYWORD
|
nonn,frac,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 16 2006
|
|
|
Search completed in 0.002 seconds
|
