Fibonacci polynomials

Fibonacci polynomials are defined recursively as follow

$F_{n}(x):=\left\{\begin{array}[]{ll}1&{\rm if~{}}n=1;\\ x&{\rm if~{}}n=2;\\ xF_{n-1}(x)+F_{n-2}(x),&{\rm if~{}}n>2.\end{array}\right.$

The main (and obvious) property of this polynomials is that $F_{n}(1)$ is $n^{\rm th}$ number in Fibonacci sequence.