We consider type II superstring theory on K3×S1×R1,4 and study perturbative BPS states in the near-horizon
background of two Neveu-Schwarz fivebranes whose world-volume wraps the K3×S1 factor. These states are counted by the spacetime helicity
supertrace χ2(τ) which we evaluate. We find a simple expression for
χ2(τ) in terms of the completion of the mock modular form
H(2)(τ) that has appeared recently in studies of the decomposition of
the elliptic genus of K3 surfaces into characters of the N=4 superconformal
algebra and which manifests a moonshine connection to the Mathieu group
M24.Comment: 32 page