  In this paper, we give the determinant expressions of the hypergeometric
Bernoulli numbers, and some relations between the hypergeometric and the
classical Bernoulli numbers which include Kummer's congruences. By applying
Trudi's formula, we have some different expressions and inversion relations. We
also determine explicit forms of convergents of the generating function of the
hypergeometric Bernoulli numbers, from which several identities for
hypergeometric Bernoulli numbers are given.
