[Math] Converting this recursive function into a non-recursive equation

I am trying to convert the following recursive function to a non-recursive equation:

$$
f(n) =
\begin{cases}
0,&\text{if n = 0;}\newline
2 \times f(n -1) + 1,&\text{otherwise.}
\end{cases}
$$

I have calculated the results for $n = 1$ through to $n = 6$ but I cannot find a discernible pattern from which to make an equation. The results are:

$$f(1) = 1$$

$$f(2) = 3$$

$$f(3) = 7$$

$$f(4) = 15$$

$$f(5) = 31$$

$$f(6) = 63$$

I hope I have formatted this correctly (my first time using LaTex), and if anyone could offer any help that would be greatly appreciated.