Proof of some conjectural congruences involving Apery-like sequences

In this paper, we evaluate Sigma(p-1)(k=1) 1/k(3) (x k) (-1 -x k) and Sigma(p-1)(k=1) 1/k(2) (x k) (-1 -x k) modulo p and modulo p(2) respectively, and by these we prove some conjectures of Z.-H. Sun involving V-n(x) = Sigma(n)(k=0) (n k) (n + k k) (-1)(k) (x k) (-1 - x k) with n = p, p-1, 2p modulo p(4) for any prime p > 3 and x = -1/3,-1/4,-1/6.