Given the sequence defined by the following recurrence relation: � 1 = 2 a 1 =2 � � = 1 � ⋅ � � − 1 a i = i 1 ⋅a i−1 for � >= 2 i>=2 Prove that � � = 2 � ! a n = n! 2 for any positive integer � n. Hint: The factorial of � n, denoted by � ! n!, is given by � ! = 1 ⋅ 2 ⋅ 3 ⋅ . . . ⋅ ( � − 1 ) ⋅ � n!=1⋅2⋅3⋅...⋅(n−1)⋅n.