def get_hippo_A(N:int) -> np.ndarray:
    A = np.zeros((N,N))
    for n in range(N):
        for k in range(N):
            if n > k:
                A[n,k] = (2*n+1)**0.5*(2*k+1)**0.5
            elif n == k:
                A[n,k] = (n+1)
    return A