52 
ME.  A.  CAYLEY  ON  THE  PAETITION  OE  NTJjHBEES. 
The  complete  expression  for  the  number  of  partitions  is  P(l,  2,  3,  4,  6,  ^)q 
jq3^(12^^+630^+1230^+1102502^+439810^+598731) 
+ 4^  (6^^+126^+581)(1,  -l)pcr2, 
+ (2, -1, -l)pcr3, 
+ 3^  (42, -19, -23)  per  3, 
+ ^ (1,  1, -1, -l)pcr4, 
+ Yb  (2,  1,  0,  -1,  -2)  per  5, 
+ ^ . . (2,  1,  -1,  —2,  -1,  l)pcr65. 
