  An extensive literature exists describing various techniques for the
evaluation of Hankel determinants. The prevailing methods such as Dodgson
condensation, continued fraction expansion, LU decomposition, all produce
product formulas when they are applicable. We mention the classic case of the
Hankel determinants with binomial entries ${3k+2 \choose k}$ and those with
entries ${3k \choose k}$; both of these classes of Hankel determinants have
product form evaluations. The intermediate case, ${3k+1 \choose k}$ has not
been evaluated. There is a good reason for this: these latter determinants do
not have product form evaluations.
  In this paper we evaluate the Hankel determinant of ${3k+1 \choose k}$. The
evaluation is a sum of a small number of products, an almost product.
  The method actually provides more, and as applications, we present the
salient points for the evaluation of a number of other Hankel determinants with
polynomial entries, along with product and almost product form evaluations at
special points.
