# find the first power of $t$ with a non-positive coefficient

Consider the following rational expression in $t$,

$$f(t)=\frac{(1-t^q)^{m-k}((1-t^2)^m}{(1-t)^{m-k+1}((1-t^{2q})^m}$$ where $q=4,m=33, k=31$.

I want to find the first power of $t$ with a non-positive coefficient. How can I proceed? The hint given in the book is that

$$f(t)=1 + 26t + 295t^2 + 1820t^3 + 5610t^4 − 1560t^5+\dots$$

How did the author of the book arrived at this approximation? Kindly give some hints. Is it possible to do it in SageMath.

Thanks for reading