It doesn't say should not multiply a number smaller than zero.

I agree.  Also what about 4!!!! = 4 ?

I dont understand why that is.  Shouldn't it be 4(4-1*4) = 0

and the last number in sequence (n%k) is apperently not a multiplier?

We want to calculate 4!!!! n=4, k=4. Second case in definition: n!!…!=n(n-k)(n-2k)…k, if k divides n. So 4!!!! = 4.

For example, 6!=6*5*4*3*2*1, 6!!=6*4*2, 6!!!=6*3, 6!!!!=6*2, 6!!!!!=6*1, 6!!!!!!=6.