What is the value of a sum similar to Basel problem but with fibonacci coefficient [closed]

The title is pretty self-explanatory. What is the value of $$\sum_{n=1}^{\infty}\frac{f_n}{n^2}$$

$$f_n$$ grows exponentially, so the sum diverges. To elaborate, if $$a_n := \dfrac{f_n}{n^2}$$, it can be shown that $$\lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n}\right| = \varphi = \frac{1+\sqrt{5}}{2} > 1,$$ and so by the ratio test, the series diverges.