The reaction rate of the stellar reaction 13C(alpha,n)16O, which is currently considered to be the main neutron source for the slow (s) process at low energies, has been rederived using the direct alpha-transfer reaction 13C(6Li,d)17O leading to the subthreshold state at 6.356 MeV in 17O. The contribution of the subthreshold state is found to be much smaller than the currently accepted predictions for the main neutron source of the s process, indicating less of a role of this reaction as the neutron source for the s-process scenario in low-mass stars at the asymptotic giant branch.