Calculating odds of rolling a given total with a specified number of dice

[Thomas Klemm]

Another approach could be to use:

\(x^5+x^4+x^3+x^2+x+1=\frac{x^6-1}{x-1}\) if \(x\ne 0\).

Now we can use the binomial formulae to calculate the coefficients of \(x^k\) for both expressions \((x^6-1)^9\) and \((x-1)^9\) and just have to implement polynomial division.

Cheers
Thomas