I am asked to find the Laurent series for
$$f(z)=\frac{\sin(z^3)}{z^4}.$$
In the deleted nehgborhood $0<\vert z \vert<R.$
So by using the series for $\sin z$ I obtain
$$\sum_{n=0}^\infty (-1)^n \frac{z^{6n-1}}{(2n+1)!}.$$
So the negative $1$ term is just $1$? And is this the correct result or do I need to reindex still?