I have stumbled upon a weird series expression. It looks like
\begin{equation} S=\sum_{i=0}^\infty{A^i}{x^{\sum_{j=0}^ij}} \end{equation}
Alternatively, it is
\begin{equation} 1+Ax+A^2x^3+A^3x^6+A^4x^{10}+\dots \end{equation}
I have no reason to believe this summation has a good closed form expression. If you prove there is no good closed form expression, I would appreciate it as well.
Thanks!