多項式乘方展開公式
下列多項式乘方展開公式之完整表述：\[\left(\sum_{i=1}^ma_i\right)^{n_0}=\sum_{1\le i\le n}^{n_i\le n_{i-1}}\prod_{i=1}^mC_{n_{i-1}}^{n_i}a_i^{n_{i-1}-n_i},\\
\forall i\in,n_i\in\mathrm{N},n_m=0.\]
以下乃冗贅形式：
\[\left(\sum_{i=1}^ma_i\right)^{n_0}=\sum_{i=1}^{r+1}T_i,T_{k+1}=\prod_{i=1}^mC_{n_{i-1}}^{n_i}a_i^{n_{i-1}-n_i},\\
k=\sum_{i=1}^{m-1}C_{n_i+m-i-1}^{n_i-1},r=k|_{n_1,n_2,\cdots,n_{m-1}=n_0}=\sum_{i=1}^{m-1}C_{n_0+m-i-1}^{n_0-1}=C_{n_0+m-1}^{n_0},\\
\forall i\in,n_i\in\mathrm{N},n_i\ge n_{i+1}\ge n_m=0.\]
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