数列an满足a1=1,当n≥2时an²-(n+2)*an-1*an+2*n*an-1²=0 求通项公式

an²-(n+2)*an-1*an+2*n*an-1²=0
因式分解得(an-2a(n-1))(an-na(n-1))
则an-2a(n-1)=0 或an-na(n-1)=0
即an=2a(n-1) 或an/a(n-1)=n
故an=2^(n-1) 或 an=n!