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Most existing end-to-end Table Question Answering (Table QA) models consist of a two-stage framework with a retriever to select relevant table candidates from a corpus and a reader to locate the correct answers from table candidates. Even though the accuracy of the reader models is significantly improved with the recent transformer-based approaches, the overall performance of such frameworks still suffers from the poor accuracy of using traditional information retrieval techniques as retrievers. To alleviate this problem, we introduce T-RAG, an end-to-end Table QA model, where a non-parametric dense vector index is fine-tuned jointly with BART, a parametric sequence-to-sequence model to generate answer tokens. Given any natural language question, T-RAG utilizes a unified pipeline to automatically search through a table corpus to directly locate the correct answer from the table cells. We apply T-RAG to recent open-domain Table QA benchmarks and demonstrate that the fine-tuned T-RAG model is able to achieve state-of-the-art performance in both the end-to-end Table QA and the table retrieval tasks.