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We compute the Morse index $\textsf{m}(u_{p})$ of any radial solution $u_{p}$of the semilinear problem: \begin{equation} \label{problemaAbstract}\tag{P}\left\{ \begin{array}{lr} -\Delta u=|x|^{\alpha}|u|^{p-1}u & \mbox{in } B\\ u=0& \mbox{ on }\partial B \end{array} \right. \end{equation} where $B$ is theunit ball of $\mathbb R^{2}$ centered at the origin, $\alpha\geq 0$ is fixedand $p>1$ is sufficiently large. In the case $\alpha=0$, i.e. for the\emph{Lane-Emden problem}, this leads to the following Morse index formula\[\textsf{m}(u_{p}) = 4m^{2}-m-2, \] for $p$ large enough, where $m$ is thenumber of nodal domains of $u$.

Morse index computation for radial solutions of the {H\'e}non problem in the disk