Here’s what I’ve tried so far: Generate a function for the roll of an n sided die:
$$P(x)=x+x^2+x^3+…+x^n$$
such that the power of $x$ indicates the side of the die in contact with the ground. Then, the number of ways to form the sum $k$ is the coefficient of $x^k$. For some $i$ dice, the sum of numbers can be found by:
$$P(x)=x(1+x+x^2+…+x^n-1)$$
$$P(x)=\frac{x(x^n-1)}{x-1}$$
$$P(x)^i=x^i(x^n-1)^i(x-1)^{-i}$$
and so gives a rough formula upon using sigma notation for $i=1$ through to $i=n$ for the coefficient of $x^k$. I’m stuck on evaluating this, nevertheless the denominator with which I should divide by to find the probability.