116 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



results for A; = 2 and 3 suggest that 



a4 = 4!(2 - a)-\S - 2a)-\4 - 3a)"' 



as = 4a4 

 Then by the first two of equations (33) 



flii^s ~ (I2R2 = Ri — 0,3 ~h 0^4 



dlRi — Ci2Rz — Rb — ^3^2 4~ O'i 



the solutions of which are 



ai = 4(24 - 23a + 3a') [(2 - a) (3 - 2a) (4 - 3a)r' 



02 = 2(72 - 23a - 10a' - 3a')[(2 - a) (3 - 2a) (4 - 3a)]-' 



By the last two of equations (33), Rq and i^7 are determined to be the 

 values given in Table II, which have been verified independently. Note 

 that for a = 0, both R^ and Rj are 1, and for a = 1, R^ = 6!, i?? = 7! 

 Table III tabulates, for /c = 2 to 5, for convenience in avoiding frac- 

 tions the symmetric functions hkj related to those above by 



hkj = Dkaj 

 with, as before, 



Dk = (2 - a)(3 - 2a) • • • [/c - (/c - l)a] 

 and oo = 1. The functions for /c = 5 were obtained by a process like 



Table III — Symmetric Functions for Exponential 

 Sums of Calls Served at Random 



ik = 2 



A; = 4 



k = 5 6jo = 120 - 326a + 329a2 _ U6a^ + 24a< 



651 = 600 - 978a + 329a2 + 146a3 - 72a< 



652 = 1200 - 978a - 172a2 + 78a3 + 72a* 

 66J = 1200 - 326a - 172a2 - 78a3 - 24a< 



654 = 600 



655 = 120 



