Generating Function for Boubaker Polynomials

Theorem
The Boubaker polynomials, defined as:
 * $\map {B_n} x = \begin{cases}

1 & : n = 0 \\ x & : n = 1 \\ x^2 + 2 & : n = 2 \\ x \map {B_{n - 1} } x - \map {B_{n - 2} } x & : n > 2 \end{cases}$

have as an ordinary generating function:
 * $\ds \map {f_{B_n, \operatorname {ORD} } } {x, t} = \sum_{n \mathop = 0}^{\infty} \map {B_n} x t^n = \frac {1 + 3 t^2} {1 + t \paren {t - x} }$

Proof
and then solve for $\map f {x, t}$.