The theory of determinants in the historical order of development, by Sir Thomas Muir.

'232 HISTORY OF THE THEORY OF DETERMINANTS
established by using the multiplication-theorem, the multiplier and
product being, in the case of the 4t1" order,
1-(m)1 (n) -(n)3.
-(-) (-)2..
1:, I-(rn)4 (m-_1). -(qn-2)2 (in,-3)1
respectively.
NAkGELSBACH, H. (1874).
[Zur independenten Darstellung der Beruoullischen Zahien. Zeitschriftf. Math. u. Phys., xix. pp. 219-233.]
From recurrence-formulae Ndgelsbach deduces four different
ways of expressing a Bernoulli number by means of a determinant,
The two simplest of the results are
B =11 31
1 ~.. 3 7..5.7(2n-+ 1).22-1
2 52 54
3 7, 74 7.
4 9, 94 96....
and
n ~~~~~~~~~~(2v2 + 1)!
= 1 3,5
1 71 73 75.
1 91 93 95
where r8, stands for r(r-1)... (r-s+1)/s!.
HAMMOND, J. (1875).
[On the relation between Bernoulli's numbers and the binomial
coefficients. Proceed. London Math. Soc., vii. pp. 9-14.]
Hammond's fundamental result is
1'~ 0 V/ \P I V//' 95// 20/1