Congruence Classes of 2-adic Valuations of Stirling Numbers of the Second Kind

We analyze congruence classes of S(n,k), the Stirling numbers of the second kind, modulo powers of 2. This analysis provides insight into a conjecture posed by Amdeberhan, Manna and Moll, which those authors established for k at most 5. We provide a framework that can be used to justify the conjecture by computational means, which we then complete for values of k between 5 and 20.