  We find a representation for the Maclaurin coefficients of the Hurwitz
zeta-function in terms of semi-convergent series involving the Bernoulli
polynomials and the Stirling numbers of the first kind. In particular, this
gives a representation for the coefficients of the Riemann zeta function. Our
main instrument is a certain series transformation formula. A similar result is
proved also for the Maclaurin coefficients of the Lerch zeta function.
