There are two natural ways to count stable pairs or Joyce–Song pairs on X=K3×C; one via weighted Euler characteristic and the other by virtual localisation of the reduced virtual class. Since X is noncompact these need not be the same. We show their generating series are related by an exponential.

As applications we prove two conjectures of Toda, and a conjecture of Tanaka–Thomas defining Vafa–Witten invariants in the semistable case.