We present a new measurement of the a-spectroscopic factor (S a) and the asymptotic normalization coefficient for the 6.356MeV 1/2 + subthreshold state of 17O through the 13C( 11B, 7Li) 17O transfer reaction and we determine the alpha-width of this state. This is believed to have a strong effect on the rate of the 13C(a, n) 16O reaction, the main neutron source for slow neutron captures (the s-process) in asymptotic giant branch (AGB) stars. Based on the new width we derive the astrophysical S-factor and the stellar rate of the 13C(a, n) 16O reaction. At a temperature of 100 MK, our rate is roughly two times larger than that by Caughlan Fowler and two times smaller than that recommended by the NACRE compilation. We use the new rate and different rates available in the literature as input in simulations of AGB stars to study their influence on the abundances of selected s-process elements and isotopic ratios. There are no changes in the final results using the different rates for the 13C(a, n) 16O reaction when the 13C burns completely in radiative conditions. When the 13C burns in convective conditions, as in stars of initial mass lower than 2 Mo and in post-AGB stars, some changes are to be expected, e.g., of up to 25 for Pb in our models. These variations will have to be carefully analyzed when more accurate stellar mixing models and more precise observational constraints are available.