  Given a prime $p\geq 5$, we reduce modulo p a convolution of order p-1 of
powers of two weighted Bernoulli numbers with Bernoulli numbers in terms of
harmonic numbers and generalized harmonic numbers. Our proof is based on
studying the p-adic expansion of the number of permutations of Sym(p-2) with an
even number of ascents, up to the modulus $p^2$.
