  The Gessel number $P(n,r)$ is the number of the paths in plane with $(1, 0)$
and $(0,1)$ steps from $(0,0)$ to $(n+r, n+r-1)$ that never touch any of the
points from the set $\{(x,x)\in \mathbb{Z}^2: x\geq r\}$. We show that there is
a close relationship between the Gessel numbers $P(n,r)$ and the super Catalan
numbers $S(n,r)$. By using new sums, we prove that an alternating convolution
of the Gessel numbers $P(n,r)$ is always divisible by \frac{1}{2}$S(n,r)$.
