  Motivated by the Hankel determinant evaluation of moment sequences, we study
a kind of Pfaffian analogue evaluation. We prove an LU-decomposition analogue
for skew-symmetric matrices, called Pfaffian decomposition. We then apply this
formula to evaluate Pfaffians related to some moment sequences of classical
orthogonal polynomials. In particular we obtain a product formula for a kind of
q-Catalan Pfaffians. We also establish a connection between our Pfaffian
formulas and certain weighted enumeration of shifted reverse plane partitions.
