Squares in (2^2-1)...(n^2-1) and p-adic valuation

Abstract

In this paper, we determine all the squares in the sequence $\{\prod_{k=2}^n(k^2-1)\}_{n=2}^\infty $. From this, one deduces that there are infinitely many squares in this sequence. We also give a formula for the $p$-adic valuation of the terms in this sequence.