已知数列{a_n}满足a₁=1，且a_na_n+1=2ⁿ，n∈N^*，则数列{a_n}的通项公式为（   ）

A：a_n=（ $\sqrt{2}$ ）^n﹣1

B：a_n=（ $\sqrt{2}$ ）ⁿ

C：a_n= $\{\begin{array}{c}{\left(\sqrt{2}\right)}^n,n为奇数\\ {\left(\sqrt{2}\right)}^{n-1},n为偶数\end{array}$

D：a_n= $\{\begin{array}{c}{\left(\sqrt{2}\right)}^{n\text{-}1},n为奇数\\ {\left(\sqrt{2}\right)}^n,n为偶数\end{array}$