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Human and constructive proof of combinatorial identities: an example from Romik
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms (2005).

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It has become customary to prove binomial identities by means of the method for automated proofs as developed by Petkovšek, Wilf and Zeilberger. In this paper, we wish to emphasize the role of "human'' and constructive proofs in contrast with the somewhat lazy attitude of relaying on "automated'' proofs. As a meaningful example, we consider the four formulas by Romik, related to Motzkin and central trinomial numbers. We show that a proof of these identities can be obtained by using the method of coefficients, a human method only requiring hand computations. 
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     author = {Merlini, D. and Sprugnoli, R. and Verri, M. C.},
     title = {Human and constructive proof of combinatorial identities: an example from {Romik}},
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Merlini, D.; Sprugnoli, R.; Verri, M. C. Human and constructive proof of combinatorial identities: an example from Romik. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms (2005). doi : 10.46298/dmtcs.3377. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3377/

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