A closed form of $\prod_{i=0}^{n-1}(a+id)$

Question

for positive integers $a$ and $d$ I need a general formula involving factorials for this product:$$\prod_{i=0}^{n-1}(a+id)$$( For example for $a=1$ and $d=2$ the product is equal to $\frac{(2n)!}{2^n n!}$ )

Answer 1

Observe that $$ \prod_{i=0}^{n-1}(a+id)=d^n\cdot\prod_{i=0}^{n-1}\left(\frac ad+i\right) $$ then one may recall that $$ \prod_{i=0}^{n-1} (x+i)=\frac{\Gamma(x+n)}{\Gamma(x)} $$ see for example the rising factorial.