\[ \prod_{j\ge0}\biggl(\sum_{k\ge0}a_{jk}z^k\biggr) =\sum_{n\ge0}z^n\,\Biggl(\sum_ {\scriptstyle k_0,k_1,\ldots\ge0\atop \scriptstyle k_0+k_1+\cdots=n} a_{0k_0}a_{1k_1}\ldots\,\Biggr). \]