It is a trial and error process.  We compare it term by term
with standard sequences that we are familiar with, and hopefully
we will find one that it compares nicely with.

2,   6, 30, 168, 1320

After much trial and error I finally tried comparing
it term by term with the sequence of factorials: 

1!, 2!, 3!,  4!,   5!, or

1,   2,  6,  24,  120

, , , ,  

2,   3,  5,   7,   11

That is the sequence of prime numbers.

So the formula for the nth term is

an =  n!(nth_prime_number)

The 6th prime number is 13, so it will be 6!×13 = 9360

Edwin