def METHOD_NAME(n, K):
    """Low-level implementation of Chebyshev polynomials of the 2nd kind."""
    ring = K.poly_ring('_0')
    x = ring._0
    seq = [ring.one, K(2)*x]
    for _ in range(2, n + 1):
        a = seq[-1]*x*K(2)
        seq.append(a - seq[-2])
    return seq[n]