ok, well i dont know if anyone will be able to help with this but i hope so.
it in my class notes for finding the steady state probability distribution of an M/M/m/n queue (erlang loss)
with arrival rate lamda and service time mu, for the second part of the proof, when m < k < n
P(k) = [lamda/(mu*m)] * P(k-1)
substituting a = lamda/mu
P(k) = (a/m) * P(k-1)
since we know k >= m that gives
P(k) = (a/m)^(k-m) * P(m)
and P(m) = [ a^m / m! ] *P (0)
which in my notes gives
P(k) = P(0) * (a^k)/[m^m * m!]
so there is something wrong somewhere, either in the proof or the formula at the end that we were trying to derive.