Asymptotic Bias in Information Estimates and the Exponential (Bell) Polynomials

We present a new derivation of the asymptotic correction for bias in the estimate of information from a finite sample. The new derivation reveals a relationship between information estimates and a sequence of polynomials with combinatorial significance, the exponential (Bell) polynomials, and helps to provide an understanding of the form and behavior of the asymptotic correction for bias.