|
|
A120784
|
|
Numerators of partial sums of Catalan numbers scaled by powers of 1/16.
|
|
2
|
|
|
1, 17, 137, 4389, 35119, 561925, 4495433, 287708141, 2301665843, 36826655919, 294613251551, 9427624079025, 75420992684203, 1206735883132973, 9653887065398089, 1235697544380650237
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Denominators are given under A120785.
From the expansion of sqrt(3)/2 = sqrt(1-1/4) = 1-(1/8)*sum(C(k)/16^k,k=0..infinity) one has r:=limit(r(n),n to infinity)= 4*(2 - sqrt(3)) = 1.071796769..., with the partial sums r(n) defined below.
|
|
LINKS
|
|
|
FORMULA
|
a(n)=numerator(r(n)), with the rationals r(n):=sum(C(k)/16^k,k=0..n) with C(k):=A000108(k) (Catalan numbers). Rationals r(n) are taken in lowest terms.
|
|
EXAMPLE
|
Rationals r(n): [1, 17/16, 137/128, 4389/4096, 35119/32768, 561925/524288, 4495433/4194304, 287708141/268435456,...].
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|