taylor series for exp(senz)

I'm getting trouble in express $\displaystyle e^{senz}$ in a taylor series about the origin..

(senz is the argument of the exponencial)

since the n-order derivate for z=0 of $\displaystyle e^{senz}$ is $\displaystyle cos^n(z) e^{senz} = 1$

and $\displaystyle e^w = \sum_{n=0}^\infty \frac{w^n}{n!}$

i thought that $\displaystyle e^{senz} = \sum_{n=0}^\infty \frac{sen^n(z)}{n!}$

the correct unswer is $\displaystyle e^{senz} = 1 + z + z^2/2 - z^4/8-z^5/15+...$

How can i get there ?