Mn11Ta4O21 is presented as the first hexagonal A-site manganite. Based on simple rules, the structure is compatible with a 14H-layer (cchchch)(2) stacking sequence that is related to BaVO3 and BaCrO3 high-pressure polymorphs. The A-site overstoichiometry is explained through difference in ionic radii sizes between Ba and Mn. Magnetic properties show two transitions at T-N1 = 88 K and T-N2 = 56 K. Neutron powder diffraction evidence two magnetic structures with purely antiferromagnetic and ferrimagnetic orders below T-N1 and T-N2, respectively. A complementary description with 14H-(hhccccc)(2) sequence of only Mn octahedra provides a direct comparison with BaMnO3-d hexagonal perovskites and naturally explains the AFM order. Below T-N2 a magneto-elastic coupling along with uniaxial negative thermal expansion are observed.