\[\sum_{n=0}^{\infty}\frac{q^{n(n+1)}}{\left(q^{2};q^{2}\right)_{n}\left(-q;q^{2%
}\right)_{n+1}}=\mbox{ coeff. of }z^{0}\mbox{ in }\frac{\left(-zq;q^{2}\right)%
_{\infty}\left(-z^{-1}q;q^{2}\right)_{\infty}\left(q^{2};q^{2}\right)_{\infty}%
}{\left(z^{-1};q^{2}\right)_{\infty}\left(-q;q^{2}\right)_{\infty}\left(z^{-1}%
q;q^{2}\right)_{\infty}}=\frac{1}{\left(-q;q^{2}\right)_{\infty}}\mbox{ coeff.%
 of }z^{0}\mbox{ in }\frac{\left(-zq;q^{2}\right)_{\infty}\left(-z^{-1}q;q^{2}%
\right)_{\infty}\left(q^{2};q^{2}\right)_{\infty}}{\left(z^{-1};q\right)_{%
\infty}}=\frac{G(q)}{\left(-q;q^{2}\right)_{\infty}},\]