The authors start with two little known results of Saalschütz giving recurrence relations for the Bernoulli numbers . The first of these results actually is contained in the second one which reads as
with certain numbers and which may be given explicitly and where . The case gives the first identity.
Then the authors express these numbers , in terms of Stirling numbers of both kinds. The also discuss results by P. G. Todorov [J. Math. Anal. Appl. 104, 309–350 (1984; Zbl 0552.10007)] of a similar taste involving Stirling numbers and of the first and second kind respectively.
Finally, using generating functions for the numbers they get for and the formula
where . From this they also derive some other formulas.