Generating hand grasps with language instructions is a widely studied topic that benefits from embodied AI and VR/AR applications. While transferring into hand articulatied object interaction (HAOI), the hand grasps synthesis requires not only object functionality but also long-term manipulation sequence along the object deformation. This paper proposes a novel HAOI sequence generation framework SynHLMA, to synthesize hand language manipulation for articulated objects. Given a complete point cloud of an articulated object, we utilize a discrete HAOI representation to model each hand object interaction frame. Along with the natural language embeddings, the representations are trained by an HAOI manipulation language model to align the grasping process with its language description in a shared representation space. A joint-aware loss is employed to ensure hand grasps follow the dynamic variations of articulated object joints. In this way, our SynHLMA achieves three typical hand manipulation tasks for articulated objects of HAOI generation, HAOI prediction and HAOI interpolation. We evaluate SynHLMA on our built HAOI-lang dataset and experimental results demonstrate the superior hand grasp sequence generation performance comparing with state-of-the-art. We also show a robotics grasp application that enables dexterous grasps execution from imitation learning using the manipulation sequence provided by our SynHLMA. Our codes and datasets will be made publicly available.