How to use Mathematica Ztransform on non-causal signal?

This is on version 7. By Nasser M. Abbasi. March 9,2010

Trying to find a ztransform for non-causal signal, unstable.

But the above is not correct result.

UPdate March 10,2010: OPPS, my mistake. Pointed out to me by Daniel from the mathgroup that Mathematica defines the Z transform from 0 to infinity and not from -infinity to +infinity. So please ignore this untill correct adjustment is made

my hand calculation:

For or

Hence

Notice that the signal is non-causal (runs backwards), and is unstable. The ROC is , hence does not include the unit circle. But the Z transform is , while Mathematica gave .