Is it Series

Chef define a function $F(n)$, where he can write $F(n)$ in the form of sum of $Pi/Qi$ for each integer $i$ ($i \ge 1$), we can define $Pi$ as the number of ways to fill $n$ positions with $i$ options at each position and Qi is number of ways to fill $i$ positions with $2$ options at each position. Formally, $Pi = i^n$, $Qi = 2^i$, $F(n)$ = $Σ Pi/Qi$ ( $i \ge 1$) As the $F(n)$ can be l