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A variation of Zeilberger's holonomic ansatz for symbolic determinantevaluations is proposed which is tailored to deal with Pfaffians. The method isalso applicable to determinants of skew-symmetric matrices, for which theoriginal approach does not work. As Zeilberger's approach is based on theLaplace expansion (cofactor expansion) of the determinant, we derive ourapproach from the cofactor expansion of the Pfaffian. To demonstrate the powerof our method, we prove, using computer algebra algorithms, some conjecturesproposed in the paper "Pfaffian decomposition and a Pfaffian analogue ofq-Catalan Hankel determinants" by Ishikawa, Tagawa, and Zeng. A minor summationformula related to partitions and Motzkin paths follows as a corollary.

Zeilberger's Holonomic Ansatz for Pfaffians