GENERATING FUNCTIONS IN' THE THEORY OF NUMBERS. 
135 
it then assumes the form— 
1 
1 
Vis 
1 
1 
1 
1 
7i3 
1 
1 
1 
1 
1 
— 
7i4 
724 
1 
1 
1 
7i,»-2 
72,»-2 
73, M-2 
1 
1 
1 
7i,k-i 
J-i.n-l 
TiJ, 1 
1 
1 
1 
n 
72,« 
73,« 
7u 
• 71,11 — 2 
7i,h-1 
7ii^ 
724 
• 72,11-2 
72,»-1 
72 n 
1 
• 7s,n-2 
73,11- 1 
73n 
1 
74,11-2 
74,11- 1 
7411 
1 
Tl, re — 2 
1 
1 
7n- 
I 
7i,n-l 
1 
1 
1 
1 
1 
1 
1 
Yl, re 
Tre — 2, re 
which involves only the 
combinations jx^y of the 
quantities 
Art. 36. The determinant is also inversely symmetrical, and not only the principal 
diagonals, but also the adjacent minor diagonals consist wholly of units. In regard 
to the occurrence of three diagonals of units, we have here the normal form of 
inversely symmetrical determinant. 
Art. 37. We have next to consider the coaxial minor of order n — 1 obtained by 
deletion of the row and s*’’ column. 
The following successive operations, which do not alter the value, have then to be 
performed— 
