I've been looking at The reconstructed evolutionary process by Nee et al. 1994 and they provide a number of equations dealing with the birth-death process, specifically the "reconstructed" birth-death process where you only have information about lineages that currently exist today.
I am interested in this equation for the likelihood of observing N lineages after time T:
What I want is the distribution of the expected number of lineages N after time T given per-lineage birth and death rates lambda and mu. I've looked around and haven't found anything providing such an equation.