44. Given an integer $n(n \geqslant 2)$. Find the largest constant $\lambda(n)$ such that: if the real number sequence $a_{0}, a_{1}, a_{2}, \cdots, a_{n}$ satisfies $0=a_{0} \leqslant a_{1} \leqslant a_{2} \leqslant \cdots \leqslant a_{n}$ and $a_{i} \geqslant \frac{1}{2}\left(a_{i-1}+a_{i+1}\right)(i=$ $1,2, \cdots, n)$, then $\left(\sum_{i=1}^{n} i a_{i}\right)^{2} \geqslant \lambda(n) \sum_{i=1}^{n} a_{i}^{2}$. (2009 China National Team Selection Test for IMO)