Proof of some conjectures of Z.-W. Sun on congruences for Apery polynomials
arXiv:1101.0983 · doi:10.1016/j.jnt.2012.02.004
Abstract
The Apery polynomials are defined by $A_n(x)=\sum_{k=0}^{n}{n\choose k}^2{n+k\choose k}^2 x^k$ for all nonnegative integers $n$. We confirm several conjectures of Z.-W. Sun on the congruences for the sum $\sum_{k=0}^{n-1}(-1)^k(2k+1) A_k(x)$ with $x\in Z$.
11 pages, to appear in Journal of Number Theory