OFFSET
0,2
COMMENTS
From the expansion of sqrt(1+1/4) = 1+(1/8)*Sum_{k>=0} C(k)/(-16)^k one has, with the partial sums r(n) are defined below, r := lim_{n->oo} r(n) = 4*(sqrt(5)-2) = 4*(2*phi-3) = 0.944271909...
Denominators coincide with the listed numbers of A120785 but may differ for higher n values.
This is the first member (p=1) of the fourth family of scaled Catalan sums with limits in Q(sqrt(5)). See the W. Lang link under A120996.
LINKS
Wolfdieter Lang, Rationals r(n) and limit.
FORMULA
a(n)=numerator(r(n)), with the rationals r(n):=Sum_{k=0..n} ((-1)^k)*C(k)/16^k with C(k):=A000108(k) (Catalan numbers). Rationals r(n) are taken in lowest terms.
EXAMPLE
Rationals r(n): [1, 15/16, 121/128, 3867/4096, 30943/32768, 495067/524288, 3960569/4194304,...].
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
Wolfdieter Lang, Jul 20 2006
STATUS
approved