Congruences concerning Jacobi polynomials and Apery-like formulae

Let p > 5 be a prime. We prove congruences modulo p(3-d) for sums of the general form Sigma((p -3)/2)(k=0) ((2k)(k))t(k)/(2k + 1)(d+1) and Sigma((p-1)/2)(k=1) ((2k)(k))t(k)/kd with d = 0, 1. We also consider the special case t = (-1)(d)/16 of the former sum, where the congruences hold modulo p(5-d)