-1,2, - 6,24, - 120720 It's troublesome to find the analytic formula of a function. Explain why

-1,2, - 6,24, - 120720 It's troublesome to find the analytic formula of a function. Explain why

（-1）^n×n!
First, the absolute values are 1, 2, 6, 24, 120 and 720
The first is gradual expansion, so it is addition or multiplication, but the expansion speed is very fast, so it can be determined to be multiplication
Multiply by 2, 3, 4, 5, 6 each time
That is, every number is a factorial form
Look at the positive and negative, odd items are negative, even items are positive, indicating that there is a power of - 1
It can be obtained by synthesis
Factorial is the calculation method from 1 to the natural number n, expressed by n! And read as "factorial of n"
That is n! = 1 × 2 × 3 × 4 × ×n