  Gessel's walks are the planar walks that move within the positive quadrant
$\mathbb{Z}_{+}^{2}$ by unit steps in any of the following directions: West,
North-East, East and South-West. In this paper, we find an explicit expression
for the trivariate generating function counting the Gessel's walks with $k\geq
0$ steps, which start at $(0,0)$ and end at a given point $(i,j) \in
\mathbb{Z}^2_+$.
