We analyze the coefficients of partition functions of Vafa-Witten theory for the complex projective plane CP^2. We experimentally study the growth of the coefficients for gauge group SU(2) and SU(3), which are examples of mock modular forms of depth 1 and 2 respectively. We also introduce the notion of "mock cusp form'', and study an example of weight 3 related to the SU(3) partition function. Numerical experiments on the first 200 coefficients suggest that the coefficients of a mock modular form of weight k grow as the coefficients of a modular form of weight k, that is to say as n^{k-1}. On the other hand the coefficients of the mock cusp form appear to grow as n^{3/2}, which exceeds the growth of classical cusp forms of weight 3. We provide bounds using saddle point analysis, which however largely exceed the experimental observation.