466 Aloysii Casoelli 



Series 6.« , . 0,0,1,10,45^41,357,784,1554,2850 etc. 



Dilll-r. I.ac. . , 0,1,9,35,9(3,216,427,770,1296 etc. 



DifVer. 2.iie. . . , 1,8,26,61,120,211,343,526 etc. 



Differ. 3. «e 7,18,35,59,91,132,183 etc 



Differ. 4.ae 11,17,24,32,41,51 etc. 



Differ. 5.ae 6,7,8,9,10 etc 



Differ. 6.»cconstaptes . . . 1,1,1,1 etc 



Series 7.a . 

 Differ. 1.»c. 

 Differ. 2.ae, 

 Differ. 3.ae. 

 Difftr. 4.ae. 

 Differ. 5.ae. 

 Differ. 6.ae. 



0,0,0,4,30,1 26, 393,1 01 6,2304,4740 etc. 

 0,0,4,26,96,267,623,1288,2436 etc 

 . 0,4,22,70,171,356,665,1143 etc 

 . 4,18,48,101,185,309,483 etc 

 , . 14,30,53,84,124,174 etc 

 . . . 16,23,31,40,50 etc 

 .... 7,8,9,10 etc 



Differ. 7.a«constantes 



1,1,1 etc. 



Series S.a . . . 0,0,0,1,15,90,357,1 107,2907,6765 etc 

 Differ. I.ae. . . 0,0,1,14,75,267,750,1800,3858 etc 

 Differ. 2.»e. . . . 0,1,1 3,61,192,483,1050,2058 etc 

 Differ. 3.»e. . . . 1,12,48,131,291,567,1003 etc 



Differ. 4.a<: 11,36,83,160,276,441 etc 



Differ. 5.ac 25,47,77,116,165 etc 



Differ. 6.ac 22,30,39,49 etc 



Differ. 7.ae 8,9,10 etc 



Differ. 8.aeconstantes .... 1,1 etc 



Hinc lemmate superlus demonstrato liabebimus terminos ge- 

 nerales harum serierum, scilicet coellicientes. A„ A,, Aj etc. 

 hoc modo expresses 



A,=(r»-1) 



^^Jm-A)i^ +2(.-1) +1 



_ (.>-1)-C».-3) 3(^-1)(^-2) _ 



2... 3 2 -T- '^ ' 



