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