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We present a systematic investigation of the crystal structure and magnetism of van der Waals topological insulators MnBi_2nTe_3n+1 (n = 1, 2) using single-crystal neutron diffraction, where emergent quantum phenomena have been recently observed. We show unambiguously that MnBi₂Te₄ orders antiferromagnetically below 24 K featured by a magnetic symmetry R_I-3c while MnBi₄Te₇ is antiferromagnetic below 13 K with a distinct magnetic space group P_c-3c1. They both present antiferromagnetically coupled ferromagnetic layers with spins along the c-axis. Further, we put forward a stacking rule for the crystal structure of an infinitely adaptive series MnBi_2nTe_3n+1 with the building unit of [Bi₂Te₃]. This enables us to draw that a two-dimensional magnetism limit might be realized in the derivatives. Our work may promote the theoretical predictions of exotic quantum states in the series of MnBi_2nTe_3n+1.