Casimir eigenvalue for sl2 ($\frac{1}{2}m(m+2)$)

For ${\mathfrak{sl}}_2$ with $[h,e]=2e$, $[h,f]=-2f$, and $[e,f]=h$, the Casimiracts on the irreducible highest-weight module $V(m)$ by the scalar $\frac{1}{2}m(m+2)$.