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
Wolfdieter Lang, Jul 20 2006
STATUS
approved