What are the next numbers in this sequence?

1,3,12,60,360,2520,...

METHOD 1:

Let the ith sequence be denoted by T(i).

Then, by the conditions of the problem:

T(i+1) = (i+2)*T(i) and, consequently:

The required missing term:

T(6)

= 8*2520

= 20160

METHOD 2:

T(1) = 1; T(i) = i!/2; since 6>1, it follows that:

T(6) = 8!/2 = 20160