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Zbl 0743.11012
Deeba, Elias Y.; Rodriguez, Dennis M.
Stirling's series and Bernoulli numbers.
(English)
[J] Am. Math. Mon. 98, No.5, 423-426 (1991). ISSN 0002-9890

For $n=2,3,\ldots$ the following infinite system of recurrences for the Bernoulli numbers $B\sb m$ is shown: $$B\sb m={1\over n(1-n\sp m)}\sum\sp{m-1}\sb{k=0}n\sp k{m\choose k}B\sb k\sum\sp{n- 1}\sb{j=1}j\sp{m-k}.$$ The proof follows by direct computations from the usual generating function of the Bernoulli numbers.
[R.F.Tichy (Graz)]
MSC 2000:
*11B68 Bernoulli numbers, etc.
05A15 Combinatorial enumeration problems

Keywords: infinite system of recurrences; Bernoulli numbers; generating function

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