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, 10:08, 19 May 2015
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| 0 & \text{otherwise} | | 0 & \text{otherwise} |
| \end{cases} | | \end{cases} |
| + | \end{align} |
| + | </math> |
| + | |
| + | Because <math>a_k</math> may be 0, we will see cases of <math>\binom{k-1}{-1}</math> when <math>a_k=0</math>. This is alright because of the definition of <math>\binom{n}{r}</math>. |
| + | But to make it more readable, we can define the function equivalently as: |
| + | |
| + | <math> |
| + | \begin{align} |
| + | G(a_1,.. , a_P) = \sum_{k=1}^P \binom{k+a_k-1}{k} |
| \end{align} | | \end{align} |
| </math> | | </math> |