def find_sigmas_from_etas(etas):
    """Compute sigmas from etas using
    k * sigma_k = \\sum_{j=1}^k (-1)^{j+1} sigma_{k-j} etas[j],  k = 1, ..., n,  where  len(etas) = n + 1."""
    n = len(etas) - 1
    sigmas = [0.] * (n + 1)
    sigmas[0] = 1.
    for k in range(1, n + 1):
        sigmas[k] = sum([(-1) ** (j + 1) * sigmas[k - j] * etas[j] for j in range(1, k + 1)]) / float(k)
    return sigmas