Sums of products of Bernoulli numbers.

*(English)*Zbl 0863.11011Closed expressions are obtained for sums of products of Bernoulli numbers of the form

$$\sum \left(\genfrac{}{}{0pt}{}{2n}{2{j}_{1},\cdots ,2{j}_{N}}\right){B}_{2{j}_{1}}\cdots {B}_{2{j}_{N}},$$

where the factor in parentheses is a multinomial coefficient and the summation is extended over all nonnegative integers ${j}_{1},\cdots ,{j}_{N}$ 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.

Reviewer: T.M.Apostol (Pasadena)

##### MSC:

11B68 | Bernoulli and Euler numbers and polynomials |