def find_next_coefficient_c(k, previous_c, lamb, beta):
    """Return  c_k = lamb^(k-1) * (1 - lamb)^(k * beta - k + 1) * \\binom{k * beta}{k - 1} / k.
    To avoid large values of  \\binom  when 'k' is sufficiently big, and to decrease the runtime,
    the value is computed as:
    с_1 = (1-lamb)^beta,
    c_k = c_{k-1} * lamb * (1 - lamb)^(beta-1) * beta * \\prod_{j=1}^{beta-1} (beta * k - j) / (beta * k - k + 2 - j).
    """
    if k == 1:
        return (1. - lamb) ** beta
    result = previous_c * lamb * (1. - lamb) ** (beta - 1) * beta
    for j in range(1, beta):
        result *= (beta * k - j) / (beta * k - k + 2. - j)
    return result