A Computer Algebra Package for Polynomial Sequence Recognition

The form of composite sequences involving combinatorial triangles and other integer sequences are common in many mathematical applications. Such composite sequences arise naturally in formulas involving sums of factorial functions and in the symbolic, polynomial expansions of the binomial coefficients and other factorial function variants. The Stirling and Eulerian number triangles also both frequently occur in applications involving finite sums and generating functions over positive powers of integers. In this thesis we provide working proof-of-concept code written in both Mathematica and Sage which can guess new identities for sequences involving special integer sequences based on the first few terms of the sequence. This approach to sequence formula guessing is not new, but our factorization-based approach based on user input and intuition provides a new wrinkle in programs for guessing formulas for sequences.