CONGRUENCES CONCERNING GENERALIZED CENTRAL TRINOMIAL COEFFICIENTS

For any n is an element of N = {0, 1, 2, ...} and b, c is an element of Z, the generalized central trinomial coefficient T-n (b,c) denotes the coefficient of x(n) in the expansion of (x(2) + bx c)(n). Let p be an odd prime. In this paper, we determine the summations Sigma T-p-1(k=0)k (b, c)(2)/m(k) modulo p(2) for integers m with certain restrictions. As applications, we confirm some conjectural congruences of Sun [Sci. China Math. 57 (2014), pp. 1375-1400].