Is this Product Notation for a Compound Sum Formula Correct?

[ktoz]

I came up with this compound sum formula

$$\frac{(m + n)!(a(n + 1) + cm)}{m!(n + 1)!}$$

and am attempting to represent it in product notation. Is the form below correct?

$$\frac{(m + n)!(a(n + 1) + cm)}{m!(n + 1)!} = (a(n + 1) + cm) \prod_{j=1}^n \frac{m + j}{j + 1}$$

Thanks

 

[AKG]

yes it is correct

 

[ktoz]

Thanks AKG