Find generating function for sequence I am suppose to find generating function for sequence $(e_n)_0^\infty$ where $e_n$ is number of ways how to write a number $n$ as a sum of four natural odd numbers ($e_n$ is basically a number of ordered fours $(\alpha, \beta, \gamma, \delta)$ odd natural numbers that $\alpha + \beta + \gamma + \delta = n$)
I don't know how should I start or "imagine" this problem. 

I’ll get you started. Consider the product
$$(x_1+x_1^3+x_1^5+\ldots)(x_2+x_2^3+x_2^5+\ldots)(x_3+x_3^3+x_3^5+\ldots)(x_4+x_4^3+x_4^5+\ldots)\;;$$
a typical term has the form $x_1^\alpha x_2^\beta x_3^\gamma x_4^\delta$, where $\alpha,\beta,\gamma$, and $\delta$ are odd positive integers. If you were to drop the subscripts on the indeterminates, that would be $x^{\alpha+\beta+\gamma+\delta}$. And if you were to collect like powers, the coefficient of $x^n$ would be the number of terms $x^{\alpha+\beta+\gamma+\delta}$ with $\alpha+\beta+\gamma+\delta=n$. In other words, it would be $e_n$. Thus,
$$\sum_{n\ge 0}e_nx^n=\left(x+x^3+x^5+\ldots\right)^4\;.$$
Can you take it from here to get the desired generating function?
