Question: bivariate generating function

Greetings to all.

Just a quick question, probably something obvious, please bear with me Your patience is appreciated.

As part of solving a posted problem at math.SE it became necessary for me to compute the bivariate generating function

sum(sum(binomial(2*q,n-1)*z^q/q!, q=0..infinity)*w^n,n=1..infinity)

The correct answer (in fact a simple computation) is

w exp(z(w+1)^2).

When asked to compute this sum with the command shown, Maple produces

hypergeom([], [], z) w

My question for you is, how does this represent the above answer that I computed manually? When I simplify the hypergeometric, Maple says

w exp(z)

which would appear to be the wrong value. Could someone enlighten me regarding this discrepancy?

BTW there seems to be no tag "hypergeometric" and I don't have enough points to create it.

Best regards, Marko Riedel