Congruences Involving Alternating Multiple Harmonic Sums
Abstract
We show that for any prime $p\neq 2$, $$\sum_{k=1}^{p-1}{(-1)^k\over k}{-{1\over 2} \choose k} \equiv -\sum_{k=1}^{(p-1)/2}{1\over k} \pmod{p^3}$$ by expressing the left-hand side as a combination of alternating multiple harmonic sums.