  We construct a natural basis for the space of weak harmonic Maass forms of
weight 5/2 on the full modular group. The non-holomorphic part of the first
element of this basis encodes the values of the ordinary partition function
p(n). We obtain a formula for the coefficients of the mock modular forms of
weight 5/2 in terms of regularized inner products of weakly holomorphic modular
forms of weight -1/2, and we obtain Hecke-type relations among these mock
modular forms.
