From [Wiki][1]:

> In the standard inertial coordinates of special relativity, for
> unidirectional motion, proper acceleration is the rate of change of
> proper velocity with respect to **coordinate time**.

You're instead finding the rate of change of proper velocity with respect to proper time and, so, are picking up an extra Lorentz factor.

  [1]: http://en.wikipedia.org/wiki/Proper_acceleration