Most of the nuclei in the mass range 90 ≲ A ≲ 208 are produced through the so-called s-process, namely through a series of neutron capture reactions on seed nuclei followed by β-decays. The 13C(α, n)16O reaction is the neutron source for the main component of the s-process. It is active inside the helium-burning shell of asymptotic giant branch stars, at temperatures ≲ 108 K, corresponding to an energy interval of 140 - 230 keV. In this region, the astrophysical S(E)-factor is dominated by the -3 keV sub-threshold resonance due to the 6.356 MeV level in 17O. Direct measurements could not soundly establish its contribution owing to the cross section suppression at astrophysical energies determined by the Coulomb barrier between interacting nuclei. Indirect measurements and extrapolations yielded inconsistent results, calling for further investigations. The Trojan Horse Method turns out to be very suited for the study of the 13C(α, n)16O reaction as it allows us to access the low as well as the negative energy re- gion, in particular in the case of resonance reactions. We have applied the Trojan HorseMethod to the 13C(6Li, n16O)d quasi-free reaction. By using the modified R-matrix approach, the asymptotic normalization coefficient {( {tilde C{α 13{{C}}}17{{O(1/}{{{2}}{ + }}{{)}}}} )^2} of the 6.356 MeV level has been deduced as well as the n-partial width, allowing to attain an unprecedented accuracy for the 13C(α, n)16O astrophysical factor. A preliminary analysis of a partial data set has lead to {( {tilde C{α 13{{C}}}17{{O(1/}{{{2}}{ + }}{{)}}}} )^2} = 6.7 - 0.6 + 0.9 {{f}}{{{m}} - 1}, slightly larger than the values in the literature, determining a 13C(α, n)16O reaction rate in agreement with the most results in the literature at ̃ 108 K, with enhanced accuracy thanks to this innovative approach.