I need some help with an assignment question:
I must determine the sequence generated by the following generating function: $2x^3 \over 1 - 5x ^ 2 $
In class we have only gone from the sequence to the closed form so, I am not really sure how to begin on this. I feel like I should begin by separating the functions so that we are working with $ 2x^3 \cdot {1 \over 1-5x^2}$ which is closer to the form that I am used to seeing come from the sequence. We would get these closed-form functions out from the sequence using a table, so logically going the other way should work the same way. In my table, I have nothing of the form $1 \over 1-ax^2$.
Thank you for any assistance.