In Marcel Proust;;s most famous novel, In Search of Lost Time, a Madeleine cake elicited in him a nostalgic memory of Combray. Here we present a computational hypothesis of how such an episodic memory is represented in a brain area called the hippocampus, and how the dynamics of the hippocampus allow the storage and recall of such past events. Using the Neural Engineering Framework (NEF), we show how different aspects of an event, after compression, are represented together by hippocampal neurons as a vector in a high dimensional memory space. Single neuron simulation results using this representation scheme match well with the observation that hippocampal neurons are tuned to both spatial and non-spatial inputs. We then show that sequences of events represented by high dimensional vectors can be stored as episodic memories in a recurrent neural network (RNN) which is structurally similar to the hippocampus. We use a state-of-the-art Hessian-Free optimization algorithm to efficiently train this RNN. At the behavioural level we also show that, consistent with T-maze experiments on rodents, the storage and retrieval of past experiences facilitate subsequent decision-making tasks.