Designing motion representations for 3D human action recognition from skeleton sequences is an important yet challenging task. An effective representation should be robust to noise, invariant to viewpoint changes and result in a good performance with low-computational demand. Two main challenges in this task include how to efficiently represent spatio-temporal patterns of skeletal movements and how to learn their discriminative features for classification tasks. This paper presents a novel skeleton-based representation and a deep learning framework for 3D action recognition using RGB-D sensors. We propose to build an action map called SPMF (Skeleton Posture-Motion Feature), which is a compact image representation built from skeleton poses and their motions. An Adaptive Histogram Equalization (AHE) algorithm is then applied on the SPMF to enhance their local patterns and form an enhanced action map, namely Enhanced-SPMF. For learning and classification tasks, we exploit Deep Convolutional Neural Networks based on the DenseNet architecture to learn directly an end-to-end mapping between input skeleton sequences and their action labels via the Enhanced-SPMFs. The proposed method is evaluated on four challenging benchmark datasets, including both individual actions, interactions, multiview and large-scale datasets. The experimental results demonstrate that the proposed method outperforms previous state-of-the-art approaches on all benchmark tasks, whilst requiring low computational time for training and inference.