已知 an=an+1+12 (n=1,2),a1,a2,a3∈[−1,1]{a}_{n} = \sqrt{\frac{{a}_{n + 1} + 1}{2}}\ (n=1,2),{a}_{1},{a}_{2},{a}_{3} \in \left\lbrack {-1,1}\right\rbrackan=2an+1+1 (n=1,2),a1,a2,a3∈[−1,1] 且 a1=cosπ9{a}_{1} = \cos \frac{\pi }{9}a1=cos9π ,则 a1a2a3{a}_{1}{a}_{2}{a}_{3}a1a2a3 的值为（ ）A. 12\frac{1}{2}21B. 14\frac{1}{4}41C. 18\frac{1}{8}81D. 116\frac{1}{16}161