Express number of ways integer can be written as coefficient in generating series Question:
"Express the number of ways that an integer $n$ can be written as a sum of a cube of an integer $s\ge-1$ plus the fourth power of an integer $t$ plus the square of an odd integer $r$ as a certain coefficient in an appropriate generating series."
So trying to simplify this convoluted question I arrive at:
Express the number of ways that an integer $n$ can be written as a sum of $s^3+t^4+r^2$ where$ -1\lt s \lt Z,t\in Z,r\in Zodd$ as a certain coefficient in an appropriate generating series.  (where $Z$ is all integers).
So I believe that the sum would be something similar to
$$\sum_{n=0}^\infty c_n(s^3+t^4+r^2)\ . $$
I think that what it's asking me to do after this is determine the coefficient $c_n$ so that it is the number of combinations of $s,j,r$ so that  $(s^3+t^4+r^2) = n$. I'm not sure how to go about this, if I'm even on the right track, or how the constraints on $s,j,r$ would come into play.  
Any help would be much appreciated, thank you.

If you look at the coefficient of $x^n$ in 
$$\sum_{i=0}^\infty x^{i^3} \sum_{j=0}^\infty x^{j^4} \sum_{k=0}^\infty x^{(2k+1)^2}$$
you will see that it will be exactly the number of ways to write $n$ in the specified way. This is what "they" want, I am pretty sure.
