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Corpus ID: 232014649

New representations for all sporadic Ap\'ery-like sequences, with applications to congruences

@inproceedings{Gorodetsky2021NewRF,
title={New representations for all sporadic Ap\'ery-like sequences, with applications to congruences},
author={Ofir Gorodetsky},
year={2021}
}

Sporadic Apéry-like sequences were discovered by Zagier, by Almkvist and Zudilin and by Cooper in their searches for integral solutions for certain families of secondand third-order differential equations. We find new representations, in terms of constant terms of powers of Laurent polynomials, for all the 15 sporadic sequences. The new representations in turn lead to binomial expressions for the sequences, which, as opposed to previous expressions, do not involve powers of 8 and powers of 3… Expand