回復 1# a0608we 的帖子
\(\begin{align}
& {{a}_{n}}=\frac{6}{2}\times \frac{10}{3}\times \frac{14}{4}\times \cdots \cdots \times \frac{4n-2}{n}\quad \left( n\ge 2 \right) \\
& =\frac{{{2}^{n-1}}\times \left( 2n-1 \right)!!}{n!} \\
& =\frac{{{2}^{n}}\times \left( 2n-1 \right)!!\times n!}{2\times n!\times n!} \\
& =\frac{\left( 2n \right)!}{2\times n!\times n!} \\
& =\frac{2n\times \left( 2n-1 \right)!}{2\times n!\times n!} \\
& =\frac{\left( 2n-1 \right)!}{n!\times \left( n-1 \right)!} \\
& =C_{n}^{2n-1} \\
\end{align}\)
是正整數
