Akm[k_,m_]:=Piecewise[{{0, k != 2 || (m != -2 && m != -1 && m != 0 && m != 1 && m != 2)}, {A[2, 2], k == 2 && (m == -2 || m == 2)}, {-A[2, 1], k == 2 && m == -1}, {A[2, 0], k == 2 && m == 0}}, A[2, 1]]