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This study presents a new technique based on Deep Learning with Recurrent Neural Networks to address the prediction of car park occupancy rate. This is an interesting problem in smart mobility and we here approach it in an innovative way, consisting in automatically design a deep network that encapsulates the behavior of the car occupancy and then is able to make an informed guess on the number of free parking spaces near to the medium time horizon. We analyze a real world case study consisting of the occupancy values of 29 car parks in Birmingham, UK, during eleven weeks and compare our results to other predictors in the state-of-the-art. The results show that our approach is accurate to the point of being useful for being used by citizens in their daily lives, as well as it outperforms the existing competitors.