Here is a way to solve it but how should I find the general form and verify it ?
The last step is the where we will conclude the general form from it and then verify it:
T(n) = nT(n-1) + 1 , T(0) = 0
T(n-1) = (n-1)T(n-2) + 1
T(n-2) = (n-2)T(n-3) + 1
T(n-3) = (n-3)T(n-4) + 1
T(n) = n[(n-1)T(n-2) + 1] + 1
T(n) = n(n-1)T(n-2) + n + 1
T(n) = n(n-1)[(n-2)T(n-3) + 1] + n + 1
T(n) = n(n-1)(n-2)T(n-3) + n(n-1) + n + 1
T(n) = n(n-1)(n-2)[(n-3)T(n-4)+1] + n(n-1) + n + 1
T(n) = n(n-1)(n-2)(n-3)T(n-4) + n(n-1)(n-2) + n(n-1) + n + 1 \
T(n) = n(n-1)(n-2)(n-3)T(n-4) + n(n-1)(n-2) + n(n-1) + n + 1