  The subcritical Markov branching process X(t) starting with one particle as
the initial condition has the ultimate extinction probability q = 1. The
branching mechanism in consideration is defined by the mixture of logarithmic
distributions on the nonnegative integers. The purpose of the present paper is
to prove that in this case the random number of particles X(t) alive at time
t>0 follows the shifted extended Sibuya distribution, with parameters depending
on the time $t>0$. The conditional limit probability is exactly the logarithmic
series distribution supported by the positive integers.
