On the divisibility properties of certain binomial sums

For any integer n>1, we prove that2n(2nn)|∑k=0n−1(6k+1)(2kk)328(n−k−1) and2n(2nn)|∑k=0n−1(120k2+34k+3)(2kk)4(4k2k)216(n−k−1). The first divisibility result confirms a conjecture of Z.-W. Sun.