Write the first 4 terms of the sequence $a_n=n^2\cdot (n-1)!$

• A. {1, 4, 18, 96}
• B. {1, 2, 6, 24}
• C. {0, 4, 18, 96}
• D. {0, 2, 6, 24}

Answer: (A)

Verified step by step guidance

1. Understand that factorials are the product of all positive integers up to a given number, denoted by \(n! = n \times (n-1) \times (n-2) \times \cdots \times 1\).
2. Identify the factorial expressions involved in the problem and write them out explicitly to see the terms clearly.
3. Look for common factors in the factorial expressions that can be canceled or simplified, such as \(\frac{n!}{(n-k)!} = n \times (n-1) \times \cdots \times (n-k+1)\).
4. Rewrite the factorial expressions using these simplifications to reduce the problem to multiplication or division of smaller numbers or expressions.
5. Perform any remaining arithmetic or algebraic operations after simplification to express the final factored form.