Notice, in the discrete case where \(R\) = {0, 1, 2, ... }
\begin{equation*}
N(t) = E[t^x] = \sum_R t^x f(x) = f(0) + t f(1) + t^2 f(x) + t^3 f(3) + ...
\end{equation*}
Therefore, by continually taking derivatives with respect to t and then evaluating those derivatives at t=0,
\begin{gather*}
N(0) = f(0)\\
N'(0) = f(1)\\
N''(0) = 2 f(2)\\
N'''(0) = 6 f(3)
\end{gather*}
etc.