Asymptotics of the Euler transform of Fibonacci numbers
Abstract
The generating function for the sequence A166861 in the OEIS (Euler transform of Fibonacci numbers) is Productk>0 1/(1-xk)F(k), where F(k) are the Fibonacci numbers. This paper analyzes the more general generating function U(x) = Productk>0 1/(1-xk)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.
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