= Solution
A <Papperitz symbol> records the three regular singular points of a second-order Fuchsian equation and the two characteristic exponents at each point. Near $z=1$, substituting $w\sim(z-1)^\rho$ into the leading terms gives
$$
\rho(2\rho-1)=0,
$$
so the exponents are $0$ and $1/2$. The same calculation at $z=-1$ gives $0$ and $1/2$. At infinity, $w\sim z^s$ gives
$$
-s^2+n^2=0,
$$
so $s=\pm n$. Since an exponent $\rho$ at infinity denotes behavior $z^{-\rho}$, these are recorded as $-n,n$. Thus the equation has P-symbol
$$
\boxed{
P\left\{\begin{matrix}
1&-1&\infty&\\
0&0&-n&z\\
\tfrac12&\tfrac12&n&
\end{matrix}\right\}.}
$$
The exponent sum is $1$, as required by the <Fuchs relation> for three singular points.
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