Can this Binomial Coefficient be written differently?

Question

I am learning crypto and came across two binomial coefficients which is scary and I would like to write them differently. I would like to either separate the two coefficients or get rid of the sum (and how is that possible?).

My goal is to simplify this as much as possible so I can work with it:

$$ \sum_{i=0}^{n-1} \binom{n-1}{i}\binom{n+i-1}{i} $$

Bonus: is there any way to change such term into a simple polynomial function?

Answer 1

Hint:

Use that $\binom{n+i-1}{i}=\binom{n+i-1}{n-1}$ and simplify the expressions