In the papers Halenka and Grabowski: 1977 and 1984 (for references see "Papers") the general procedure of calculation for more realistic [as in papers, H.W. Darwin and P. Felenbok: 1965, Data for Plasma in Local Thermodynamic Equilibrium, (Gauthier-Villas, Paris); and A.W. Irwin: 1981, Astrophys. J. Suppl. Ser. 45,621] numerical values of the Atomic Partition Function (APF) has been described and applied to tin and iron. In the procedure, a simple cut-off approach to the Lowering of the Ionization Energy (LIE) is maintained. The novelty consist in taking into account all the bound quantum states of a considered system (atom or ion), and including the levels above the normal continuum. The effect of these last, many-electron excitation states on APF-values U(r) (r=1, 2, ..., for atom, single charged ion, etc.) is especially strong for elements of low normal ionization energies and of complex energetic structure, as elements of the first transition group. Detailed description was presented in series of papers: for chromium (Halenka and Grabowski, 1986), for titanium and vanadium (Halenka, 1988), for manganese and cobalt (Halenka, 1989), for iron (Madej, Halenka and Grabowski, 1999) and for nickel (Halenka and Madej, 2001).