number theory – Coefficients for the result of the multiplication of n different binomials

I have the roots of a polynomial of degree n, all the roots having the multiplicity 1, I can get the original polynomial by multiplying the following binomials: $ (z-z_0) * (z-z_1) * … * (z-z_n) $ or $ z_0, z_1, …, z_n $ are the roots of my polynomial
My question is: is there a way to calculate the coefficients of the resulting polynomial?
So, for example, if the result of the product of n binomials leads to: $ a_n * z ^ n + a_ {n-1} * z ^ {n-1} + … + a_0 $ Is there a formula for the $ a_n, a_ {n-1}, … a_0 $
Preferably, a compact formula so that I can program it.

Thank you.