[580 
580] 
PARTIALLY SYMMETRICAL DETERMINANT. 
189 
terms 
0), 
0, we 
Developing as far as A, the numerical process is 
1 
1 
1 
1 
1 
1 
1 
2 
8 
48 
384 
5840 
46080 
1 
1 
4 
1 
3? 
1 
384 
1 
* 
1 
8 
! 
ao| 
1 
384 
5540 
1 
46 080 
1 
1 
1 
1 
1 
4 
5 
3? 
T52 
1535 
1 
55 
1 
64 
1 
2o<> 
1 
384 
1 
* 
3 
7 
27 
331 
8 
45 
1280 
4<j080 
1 
1 
3 
5 
35 
6 3 
231 
2 
5 
16 
125 
556 
1024 
1 
* 
3 
7 
2 5 
2 7 
3 3 1 
8 
48 
384 
1280 
46080 
* 
1 
4 
3 
T5 
7 
55 
25 
768 
27 
2 56 0 
3 
_s_ 
16 
9 
7 
2ft 
8 
64 
128 
1024 
.5 
T5 
5 
35 
ITS 
fis 
3ft 
3ft 
10ft 
128 
2 55 
1024 
6 3 
63 
256 
ftT5 
231 
To5'i 
1 
1 
1 
ft 
5 
17 
2 4 
73 
150 
07 
185 
1 
1 
2 
6 
24 
120 
720 
1 
1 
2 
5 
17 
73 
388, 
agreeing with the former values. 
The expression of cp (m, 0) once found, it is easy thence to obtain 
e $x+l& 
6 (m, 1) = 1.2 ... .m coefft. x m in -7 
(1 — xy 
2gJ*+i** 
</> (m, 2) = 1.2 .... m coefft. x m in - 6 
(!-«)* 
2 3e ix+ix * 
6 (m, 3) = 1.2 .... m coefft. x m in — =- 
r V ' (1 - xf 
and so on, the law being obvious. 
[Addition, p. 335.] The generating function 
qqII 05#+T# 2 
«, ^i + u,«+ 1 2