def METHOD_NAME(n, k, q=None):
    r"""
    Return the `q`-binomial coefficient.
    Let `[n]_q!` denote the `q`-factorial of `n` given by
    :meth:`sage.algebras.quantum_groups.q_numbers.q_factorial()`.
    The `q`-binomial coefficient is defined by
    .. MATH::
        \begin{bmatrix} n \\ k \end{bmatrix}_q
        = \frac{[n]_q!}{[n-k]_q! \cdot [k]_q!}.
    INPUT:
    - ``n, k`` -- the nonnegative integers `n` and `k` defined above
    - ``q`` -- (default: `q \in \ZZ[q, q^{-1}]`) the parameter `q`
      (should be invertible)
    If ``q`` is unspecified, then it is taken to be the generator `q` for
    a Laurent polynomial ring over the integers.
    .. NOTE::
        This is not the "usual" `q`-binomial but a variant
        useful for quantum groups. For the version used in
        combinatorics, see :mod:`sage.combinat.q_analogues`.
    .. WARNING::
        This method uses division by `q`-factorials.
        If `[k]_q!` or `[n-k]_q!` are zero-divisors, or
        division is not implemented in the ring containing `q`,
        then it will not work.
    EXAMPLES::
        sage: from sage.algebras.quantum_groups.q_numbers import q_binomial
        sage: q_binomial(2, 1)
        q^-1 + q
        sage: q_binomial(2, 0)
        1
        sage: q_binomial(4, 1)
        q^-3 + q^-1 + q + q^3
        sage: q_binomial(4, 3)
        q^-3 + q^-1 + q + q^3
    TESTS::
        sage: from sage.algebras.quantum_groups.q_numbers import q_binomial
        sage: all(q_binomial(n, k, 1) == binomial(n, k) for n in range(7) for k in range(n+1))
        True
        sage: q_binomial(-2, 1)
        Traceback (most recent call last):
        ...
        ValueError: n must be nonnegative
    """
    # sanity checks
    if not (n in ZZ and k in ZZ):
        raise ValueError("arguments ({}, {}) must be integers".format(n, k))
    if n < 0:
        raise ValueError('n must be nonnegative')
    if not (0 <= k and k <= n):
        return 0
    k = min(n - k, k) # Pick the smallest k
    denomin = q_factorial(n - k, q) * q_factorial(k, q)
    numerat = q_factorial(n, q)
    try:
        return numerat // denomin
    except TypeError:
        return numerat / denomin