  The bivariate series $\theta (q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j$
defines a {\em partial theta function}. For fixed $q$ ($|q|<1$), $\theta (q,.)$
is an entire function. We prove a property of stabilization of the coefficients
of the Laurent series in $q$ of the zeros of $\theta$. These series are of the
form $-q^{-j}+(-1)^jq^{j(j-1)/2}(1+\sum _{k=1}^{\infty}g_{j,k}q^k)$. The
coefficients of the stabilized series are expressed by the positive integers
$r_k$ giving the number of partitions into parts of three different kinds. They
satisfy the recurrence relation $r_k=\sum _{\nu =1}^{\infty}(-1)^{\nu -1}(2\nu
+1)r_{k-\nu (\nu +1)/2}$. Set $(H_{m,j})~:~(\sum _{k=0}^{\infty}r_kq^k)
(1-q^{j+1}+q^{2j+3}-\cdots +(-1)^{m-1}q^{(m-1)j+m(m-1)/2})= \sum
_{k=0}^{\infty}\tilde{r}_{k;m,j}q^k$. Then for $k\leq (m+2j)(m+1)/2-1-j$ and
$j\geq (2m-1+\sqrt{8m^2+1})/2$ one has $g_{j,k}=\tilde{r}_{k;m,j}$.
