Let p>5 be a prime. We prove congruences modulo p3−d for sums of the
general form ∑k=0(p−3)/2(k2k)tk/(2k+1)d+1 and
∑k=1(p−1)/2(k2k)tk/kd with d=0,1. We also consider the
special case t=(−1)d/16 of the former sum, where the congruences hold
modulo p5−d.Comment: to appear in Int. J. Number Theor