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For a given sequence $a_n$, the sequence of Hankel determinants $h_n=\det [a_{i+j}]_{0\leq i,j \leq n}$ is known as Hankel transform. We consider the Hankel transform evaluation of a sequences based on the Motzkin and Catalan numbers. Computation is done using the method based on orthogonal polynomials (continued fractions) and transformations of the weight function. It is also investigated the connection between Hankel and aerating transformations.

Hankel determinants, orthogonal polynomials, weight function