  While considering nonlinear coherent states with specific anti-holomorphic
coefficients $\bar{z}^n/\sqrt{x_n!}$, we identify as first associated
Meixner-Pollaczek polynomials the orthogonal polynomials arising from shift
operators which are defined by the sequence $x_n=(n+1)^2$ . We give a formula
defining these polynomials by writing down their generating function. This also
leads to construct a Bargmann-type integral transform whose kernel is given in
terms of a $\Psi_1$ Humbert's function.
