In this paper, we obtain super congruences ∑ k=1 [ ( p−1 )/r ] ( −1 ) k+1 ( αp−1 k ) H k 2 ( mod p 2 ) and ∑ k=1 [ ( p−1 )/r ] ( −1 ) k k ( αp−1 k ) H k 2 ( mod p 2 ) , where r ∈ {1, 2, 3} and α is a ...