Sums of products of Bernoulli numbers

Closed expressions are obtained for sums of products of Bernoulli numbers of the form Sigma((2n)(2j1, ..., 2jN)) B-2j1 ... B-2jN, where the summation is extended over all nonnegative integers j(1), ..., j(N) with j(1) + j(2) + ... + j(N) = n. Corresponding results are derived for Bernoulli polynomials, and for Euler numbers and polynomials. As easy corollaries we obtain formulas for sums of products of the Riemann zeta function at even integers and of other related infinite series. (C) 1996 Academic Press, Inc.