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Synthetic data can be used in various applications, such as correcting bias datasets or replacing scarce original data for simulation purposes. Generative Adversarial Networks (GANs) are considered state-of-the-art for developing generative models. However, these deep learning models are data-driven, and it is, thus, difficult to control the generation process. It can, therefore, lead to the following issues: lack of representativity in the generated data, the introduction of bias, and the possibility of overfitting the sample's noise. This article presents the Directed Acyclic Tabular GAN (DATGAN) to address these limitations by integrating expert knowledge in deep learning models for synthetic tabular data generation. This approach allows the interactions between variables to be specified explicitly using a Directed Acyclic Graph (DAG). The DAG is then converted to a network of modified Long Short-Term Memory (LSTM) cells to accept multiple inputs. Multiple DATGAN versions are systematically tested on multiple assessment metrics. We show that the best versions of the DATGAN outperform state-of-the-art generative models on multiple case studies. Finally, we show how the DAG can create hypothetical synthetic datasets.