This paper proposes a practical approach to addressing limitations posed by using of single-channel electroencephalography (EEG) for sleep stage classification. EEG-based characterizations of sleep stage progression contribute the diagnosis and monitoring of the many pathologies of sleep. Several prior reports explored ways of automating the analysis of sleep EEG and of reducing the complexity of the data needed for reliable discrimination of sleep stages at lower cost in the home. However, these reports have involved recordings from electrodes placed on the cranial vertex or occiput, which are both uncomfortable and difficult to position. Previous studies of sleep stage scoring that used only frontal electrodes with a hierarchical decision tree motivated this paper, in which we have taken advantage of rectifier neural network for detecting hierarchical features and long short-term memory (LSTM) network for sequential data learning to optimize classification performance with single-channel recordings. After exploring alternative electrode placements, we found a comfortable configuration of a single-channel EEG on the forehead and have shown that it can be integrated with additional electrodes for simultaneous recording of the electrooculogram (EOG). Evaluation of data from 62 people (with 494 hours sleep) demonstrated better performance of our analytical algorithm than is available from existing approaches with vertex or occipital electrode placements. Use of this recording configuration with neural network deconvolution promises to make clinically indicated home sleep studies practical.