Recurrences for the Bernoulli and Euler numbers.

(1.2) J Ar(n)Bn_r = A(n), r=0 where k is independent of n and the Ar(ri), A (n) are polynomials in n with integral coefficients. It suffices to assume that (1. 2) holds for all n > ΛΟ, where n0 is fixed. The proof of this result makes use of the Staudt-Clausen theorem for the Bernoulli numbers. As a corollary of this result we prove the impossibility of a recurrence of the form (1. 2) for the Bernoulli numbers 1?̂ , of order i, where t is an arbitrary positive integer. We show also that a corresponding result holds for the Euler numbers and indeed for the Euler numbers of order t defined by