  The generating function for the sequence A166861 in the OEIS (Euler transform
of Fibonacci numbers) is Product_{k>0} 1/(1-x^k)^F(k), where F(k) are the
Fibonacci numbers. This paper analyzes the more general generating function
U(x) = Product_{k>0} 1/(1-x^k)^F(k+z), where z is a nonnegative integer, which
provides asymptotics for the sequences A166861 (z=0), A200544 (z=1) and A260787
(z=2) in the OEIS.
