  We introduce a kind of $(p, q, t)$-Catalan numbers of Type A by generalizing
the Jacobian type continued fraction formula, we proved that the corresponding
expansions could be expressed by the polynomials counting permutations on
$\S_n(321)$ by various descent statistics. Moreover, we introduce a kind of
$(p, q, t)$-Catalan numbers of Type B by generalizing the Jacobian type
continued fraction formula, we proved that the Taylor coefficients and their
$\gamma$-coefficients could be expressed by the polynomials counting
permutations on $\S_n(3124, 4123, 3142, 4132)$ by various descent statistics.
Our methods include permutation enumeration techniques involving variations of
bijections from permutation patterns to labeled Motzkin paths and modified
Foata-Strehl action.
