16. Given $x_{i} \in\{1,-1\}, i=1,2,3 \cdots \cdots, 2 n$, and $x_{1}+x_{2}+\cdots \cdots+$ $x_{i} \geqslant 0$, where $i=1,2,3 \cdots \cdots, 2 n-1, x_{1}+x_{2}+x_{3}+\cdots \cdots+x_{2 n}=0$, find the number of ordered tuples $\left(x_{1}, x_{2}, x_{3}, \cdots \cdots, x_{2 n}\right)$.
16. It can also correspond to a set of broken lines, the initial state corresponds to 0, if $x_{i}=1$, then connect a segment of the diagonal with a slope of 1; if $x_{i}=-1$, then connect a segment of the diagonal with a slope of -1, the endpoint of the entire broken line is $P(2 n, 0)$ and the broken line cannot have any common points with $y=-1$, the final result is $\frac{1}{n+1} C_{2 n}^{n}$.