You're after Pochhammer:
Pochhammer[a, 5]
(* a (1 + a) (2 + a) (3 + a) (4 + a) *)
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...