Clear[r, re, p, pmax, delta, imagesize, delta]
ClearSystemCache[]
re[0, r_] := Sqrt[8/Pi]*((1 - r)/r)^(1/4)*1;
re[1, r_] := Sqrt[8/Pi]*((1 - r)/r)^(1/4)*-1*2*(1 - 2*r);
re[p_, r_] := re[p, r] = Sqrt[8/Pi]*((1 - r)/r)^(1/4)*(-1)^p*(re[1, r]*re[p - 1, r] - re[p - 2, r]);
imagesize = 32;
pmax = 10;
delta = 2/imagesize;
Table[r = Sqrt[x^2 + y^2]; re[pmax, r], {x, -1 + delta/2, 1 - delta/2, delta}, {y, 1 - delta/2, -1 + delta/2, -delta}];