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Sums of products of Bernoulli numbers. (English) Zbl 0863.11011

Closed expressions are obtained for sums of products of Bernoulli numbers of the form

2n 2j 1 ,,2j N B 2j 1 B 2j N ,

where the factor in parentheses is a multinomial coefficient and the summation is extended over all nonnegative integers j 1 ,,j N whose sum is n. Corresponding results are derived for Bernoulli polynomials, and for Euler numbers and polynomials. Sums of this type were previously studied by Euler for n=2, and by others for n=3 and 4.


MSC:
11B68Bernoulli and Euler numbers and polynomials