A (Human!) Proof of A Conjectured Triple Sum Identity Made By Juan Sebastian Pereyra

By Doron Zeilberger

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(Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger)

Written: March 5, 2013.

It is nice, once in awhile to do things the old-fashioned way. When Juan Sebastian Pereyra asked me whether my computer can do a certain triple sum, that he encountered in his collaboration with Federico Echenique I told him that it sure could, but this particular triple sum could be done just as easily by hand, but I am too lazy to do it, and I don't want to bother Shalosh. But if he (or Federico, or both) would be willing to donate 200 dollars to the OEIS foundation as a "fee", I'll be glad to do it. He graciously agreed, and this is the result.

Added April 16, 2013: Read the very interesting paper by Federico Echenique and Juan Sebastian Pereyra where they use the identity proved here, and present a more detailed version of the proof (Lemma 3, starting on p. 20).
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