\[p\left(n\right)=\frac{1}{\pi\sqrt{2}}\sum_{k=1}^{\infty}\sqrt{k}A_{k}(n)\*%
\left[\frac{\mathrm{d}}{\mathrm{d}t}\frac{\sinh\left(\ifrac{K\sqrt{t}}{k}%
\right)}{\sqrt{t}}\right]_{t=n-(1/24)},\]