  To a higher Landau Level corresponds a generalization of the Poisson
distribution arising from generalized coherent states. In this paper, we write
down the atomic decomposition of this probability measure and expressed its
weights through 2F2 hypergeometric polynomials. Then, we prove that it is not
infinitely divisible in opposite to the Poisson distribution corresponding to
the lowest Landau level. We also derive the Levy-Kintchine representation of
its characteristic function when the latter does not vanish and deduce that the
representative measure is signed. By considering the total variation of the
last measure, we obtain the characteristic function of a new infinitely
divisible discrete probability distribution for which we compute also the
weights.
