  Lin and Chang gave a generating function of convex polyominoes with an $m+1$
by $n+1$ minimal bounding rectangle. Gessel showed that their result implies
that the number of such polyominoes is $$ \frac{m+n+mn}{m+n}{2m+2n\choose
2m}-\frac{2mn}{m+n}{m+n\choose m}^2. $$ We show that this result can be derived
from some binomial coefficients identities related to the generating function
of Jacobi polynomials.
