# Meaning of choose function with a negative number

I have encountered an expression for an inverse Laplace transform, and now I am wondering whether it is correct or maybe there is some error. More likely I don't understand it. so here goes:

$$g(p)(e^{ap}+\beta)^{-c} \Leftrightarrow \sum_{0\leq n\leq t/a -c}\left(\begin{array}[c] - -c\\ n\end{array}\right)\beta^n f(t-ac-an)$$

Where $$a,c>0$$.

So what is the meaning of this? Anyone?

Thanks

The definition of $$\binom xn$$ is $$\binom xn=\frac{x(x-1)(x-2)\cdots(x-n+1)}{n!}$$ for any nonnegative integer $$n$$ and any complex number $$x$$.