What will be a more meaningful way to represent a O$\frac{n-8}{2} \choose \frac{n}{4}-2$ Time Complexity

Question

I completed the Time Analysis for an algorithm and wanted to check if i can represent its TC in a more readable way.

The best I have at the moment is O$\frac{n-8}{2} \choose \frac{n}{4}-2$

What could be are 'easier' way to represent this TC?

Answer 1

This

$${{\frac{n-8}{2}} \choose {\frac{n}{4}-2}} \quad \in \quad \theta(2^{\frac{n}{2}} \left(\sqrt{n}\right)^{-1})$$

[Informally, the "$-\frac{8}{2}$" and the "$-2$" don't change the asymptotics]