Sequences of binomial coefficients modulo prime

The behavior of infinite sequences of binomial coefficients ((x) (y)) mod p, x = 0, 1, 2, ... ; p is a prime number) is considered. In the search of regularities, preliminary mathematical experiments are carried out using Wolfram Mathematica. The periodicity of these sequences is proved and the length of the period is determined as p to the power of [log(p) (y) ] + 1.