The number by which each number is multiplied to obtain the next number starts at 1 and increases each time. Let the terms of the series be s(1), s(2), s(3) etc. Then we have:
s(1) = 1.
s(2) = 1*s(1) = 1*1 = 1.
s(3) = 2*s(2) = 2*1 =2.
s(4) = 3*s(3) = 3*2 = 6.
s(5) = 4*s(4) = 4*6 = 24.
s(6) = 5*s(5) = 5*24 = 120.
s(7) = 6*s(6) = 6*120 = 720.
The series can be succinctly defined using the following recursive formula:
s1 = 1.
s(n) = (n-1)*s(n-1), where n is an integer greater than or equal to 2.
Actually, the next number is 120; the number after that is 720.