Find Laurent series in the deleted neighborhood $0<\vert z \vert<R$.

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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?