SCHWEITZER 1999 Problem 5

Let $\alpha>-2$ , $n\in \mathbb{N}$ and $y_1,\cdots,y_n$ be the solutions to the system of equations: $\sum_{j=1}^n \frac{y_j}{j+k+\alpha}= \frac{1}{n+1+k+\alpha}$ , $k=1,\cdots,n$ Prove that $y_{j-1}y_{j+1}\leq y_j^2 \,\forall 1<j<n$