I'm reading the classical Feynman's lectures on hydrogen atom, and I want to calculate the radial component of the wave function with the formula (19.53)
$$ F_{n,l}(\rho)=\frac{e^{-\alpha\rho}}{\rho}\sum_{k=l+1}^n a_k \rho^k $$ for $n=2$ and $l=1$. So I have $\alpha=1/n=1/2$ and $$ F_{2,1}(\rho)=\frac{e^{-\rho/2}}{\rho}a_2 \rho^2 $$ where $a_2$ should be given by the formula (19.50): $$ a_{k+1} =\frac{2(\alpha k-1)}{k(k+1)-l(l+1)} a_k $$ but, for $k+1=2$ and $l=1$ the denominator becomes $0$.
It seems that I have some stupid mistake, but I don't see where. Someone can help me?