Acting on a suggestion of \textit{V. Namias} [Am. Math. Mon. 93, 25--29 (1986; Zbl 0615.05010)] the authors use the multiplication formula for the gamma function to derive the following family of recursions for Bernoulli numbers obtained by \textit{F. T. Howard} [J. Number Theory 52, No. 1, 157--172 (1995; Zbl 0844.11019)]: \[ B_s= {1\over k(1-k^s)} \sum^{s-1}_{m= 0} {s\choose m} k^m B_m \sum^{k-1}_{j=1} j^{s- m}, \] where \(k= 2,3,\dots\)\ . Namias treated \(k= 2\) and \(k= 3\).