Since 2001, the neutron time-of-flight facility n_TOF at CERN has carried out a large number of cross section measurements of interest for several research fields, including Nuclear Astrophysics. The results of these measurements have improved our knowledge on the nucleosynthesis of chemical elements. Particularly relevant for the s-process, reported cross sections were used to constrain the Big Bang nucleosynthesis, to benchmark stellar models against nucleosynthesis in quiet and explosive scenarios, to interpret meteoritic abundances, as well as to study the neutron source reactions in Red Giant stars. After a brief description of the n_TOF facility and the related astrophysical program, the research activities about the ¹³C(a,n)¹⁶O and ²²Ne(a,n)²⁵Mg neutron source reactions are discussed.