Wireless communication systems are increasingly adopting orthogonal frequency division multiplexing (OFDM) to enable efficient high-data rate transmissions. Such systems often employ pilot symbols to estimate wireless channels, and null subcarriers on band edges to reduce adjacent channel interference. Recent work has focused on designing the pilot sequence to improve channel estimation performance. In this paper, we present a new pilot design for OFDM systems based on a arbitrary-order polynomial parameterization of the pilot subcarrier indices. We show our design achieves better performance than existing methods. Theoretical models and simulated performance demonstrate the increased accuracy of our design.