You're after *Pochhammer*:

 Pochhammer[a, 5]
 
 (* a (1 + a) (2 + a) (3 + a) (4 + a) *)

Do note, the *Mathematica* definition by default is opposite that used in many fields: it is the *Rising Factorial*, while the traditional form can be confused with *Falling Factorial*, the perhaps more common use of *Pochhammer*...