  Consider a pure birth process with intensities {\lambda}(k) =1/(1+k), with
k=0,1,2,..., we show that the subordinated chain is assimilable to a
Bernoullian scheme with dependent successes probabilities, also we show a
direct link with a degenerate Polya urn replacement scheme \cite{Janson}. We
compute explicitly transition probabilities, by generating function method, of
the subordinated chain and give some interesting bounds using the "centering
sequence" approach proposed by MacDiarmid \cite{McDiarmidcentering}.
