Local cohomology of the affine plane supported at the origin ($H_{(x,y)}^i(k[x,y])$)

For $X=\mathrm{Spec}k[x,y]$ and $Z=V(x,y)$, the only nonzero local cohomology group of the structure sheaf isIt has basis $x^{-a}{y}^{-b}$ for $a,b\ge 1$. The two-standard-open Čech cochain complex of the punctured affine plane proves the formula.