572 BELL SYSTEM TECHNICAL JOURNAL 



we know that <2(0, 0) = 1. Hence 



A{A,c- 1) 



etc. 



+ (45^2 4- 60w + 25) (" "^ "^ ^ ) 



+ (105..; + 105) ( ' t ^ ) + 105 ( ' t ^ ) 



As yet the value of w has not been specified. Since when ni is an 

 odd number and w = — (c — l)/2, the equation 



^c-l(^)c-l+7« :^ (^_ \)m^c-\(^_ ^ _ ^ _|_ l^c-l+m 



gives us 



f ^\ c— l+m 



= 0, 



let us write w = (d/l) — {c — l)/2, leaving d arbitrary; we obtain 



240 

 etc. Finally, for c? = 0, or w = — (c — l)/2, 



^(0, c - 1) = 1, A{\, c - 1) = 0, 



""■^^^^ ^(3, c-l) = 0, 



^(5, c - 1) = 



^(2,.-:) = (^ + i) 



^(4, c - 1) 



c + 3\ / 5c - 7 

 5 / I 48 



etc. 



