Each row of the Lower triangle matrix $L$ contains the binomial coefficient padded with zero. $L_{i,j} = {i \choose j}$.
Define the reciprocal inner product of $\frac{\vec{v}}{\vec{w}}$ where $\vec{v}, \vec{w} \in \mathbb{R}^n$ as $\sum_{i=0}^{n-1} \frac{\vec{v}[i]}{\vec{w}[i]} $.
Since the last row of $L$ contains all nonzero elements, now my question is, for any row $j$, what's the general formula $\frac{L_j}{L_n}$?
Here $L_j$ is the $j$th row of $L$