Tuesday, October 25, 2016

combinatorics - How to simplify this triple summation containing binomial coefficients?


\large\sum_{i=0}^{n} \sum_{j=i}^{n} \sum_{k=j}^{n} \binom{i+m-1}{m-1}\binom{j+m-1}{m-1}\binom{k+m-1}{m-1}





How to solve it when this involve more than thousand summation ?

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