Abstract
We introduce the class of nested polynomially recurrent sequences which includes a large number of sequences that are of combinatorial interest. We present an algorithm for deciding zero equivalence of these sequences, thereby providing a new algorithm for proving identities among combinatorial sequences: In order to prove an identity, decide by the algorithm whether the difference of lefthand-side and righthand-side is identically zero. This algorithm is able to treat mathematical objects which are not covered by any other known symbolic method for proving combinatorial identities. Despite its theoretical flavor and high complexity, an implementation of the algorithm can be successfully applied to nontrivial examples.
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