The H2CO center dot center dot center dot(HF)(n) (n = 1, ..., 9) complexes were investigated using the MP2 method and the following basis sets: 6-311++G(d,p), aug-cc-pVDZ and aug-cc-pVTZ. It was found that the cooperativity effect enhances significantly the F-H center dot center dot O hydrogen bond; in some of cases one can detect the covalent nature of hydrogen bonding. To deepen the nature of the interactions investigated, the scheme of decomposition of the interaction energy was applied; for stronger H-bonds where the coopearativity is more important, the delocalization energy term increases. The ratio of delocalization energy to electrostatic energy increases for stronger hydrogen bonds where the proton center dot center dot acceptor distance is shorter. The Bader theory was also applied, and it was found that for stronger H-bonds the electronic energy density at the proton center dot center dot center dot acceptor bond critical point is negative and may be attributed to the partly covalent interaction.