So I have 30 balls to divide into 4 cells. What are the number of options they must be divided under the following conditions: For each cell: u at position i so that: 4>=i>=1 Necessarily holds: i=<u<=10i (I know the answer is 1481, but the proof is difficult. In any case, the question has a requirement to use a generating function, that's why I wrote
f(x)=(x+...+x^10)(x^2+...+x^20)(x^3+....x^30)(x^4+.... +x^40) In order to find the coefficient of x^30, But from then on, I got into trouble. I would appreciate help with the question.
