 Erlang loss formula

For capacity $C$ and offered traffic $a$, the probability of a full single-resource loss system is $E(a,C)=(a^C/C!)/({\sum }_{k=0}^C{a}^k/k!)$. The stable recursion is $E(a,0)=1$, $E(a,k)=aE(a,k-1)/(k+aE(a,k-1))$.