In this paper, we derive a formula for the generating function of powers of a second-order linear recurrence sequence, with initial conditions 0 and 1. As an example, we find the generating function of the powers of the nonnegative integers. We also find new formulas for computing Eulerian polynomials.
|Journal||Journal of Integer Sequences|
|State||Published - Jan 1 2018|
- Eulerian polynomial
- Generating function
- Pascal triangle
- Second-order recurrence sequence