[154 
512 
SUPPLEMENTARY RESEARCHES ON THE PARTITION OF NUMBERS. 
The complete expression for the number of partitions is P (1, 2, 3, 4, 5, 6) q 
—!^ 0 (12q 5 + 630? 4 + 12302 s + H02502 2 + 439810? + 598731) 
+ 
1 
4608 
(6? 2 +126? +581) (1 
, 1) per 2q 
+ 
1 
162 
? ( 2 > ~ h - 
- 1) per 3g 
+ 
1 
324 
(42, - 19, - 
23) per S q 
+ 
1 
32 
(1, 1, -1, 
— 1) per 4 ( 
+ 
1 
25 
(2, 1, 0, - 1, 
— 2) per 5, 
+ 
1 
36 
..(2, 1,-1,-2, - 
1, 1) per 6,