OFFSET
1,3
COMMENTS
Denominators are b(n) = Prod[k=1..n, F(k)*F(k+1)] and a(n)/b(n) approaches (sqrt(5)-1)/2.
Can a(n) be expressed in terms of F(n), without the sum? However, the sequence appears not to be C-finite.
LINKS
Colin Barker, Table of n, a(n) for n = 1..69
PROG
(PARI) a(n) = local(f, d, nu); f=sum(k=1, n, -(-1)^k*1 / fibonacci(k) / fibonacci(k+1)); d=denominator(f); nu=numerator(f); prod(k=1, n, fibonacci(k)*fibonacci(k+1))/d*nu
CROSSREFS
KEYWORD
nonn
AUTHOR
Ralf Stephan, Jul 11 2004
STATUS
approved