Linear recurrence with polynomial coefficients

Summary

A linear recurrence with polynomial coefficients relates consecutive terms of a sequence linearly, with coefficients that are polynomials in the index $n$. It generalizes the linear recurrences with constant coefficients and covers many sequences of combinatorics, such as factorials, Catalan numbers and harmonic numbers. The sequences that satisfy such a recurrence are the holonomic sequences, and their generating functions are holonomic functions. Computer algebra uses these recurrences as finite descriptions of infinite sequences.