title: A new look at the coefficients of a reciprocal generating function.
abstract: We study a special property of free cumulants. We prove that coefficients of a reciprocal generating function correspond to "free cumulants with the first two elements in the same block."
authors.affiliation: Department of Mathematics and Cybernetics, Wroclaw University of Economics, Komandorska 118/120, 53-345 Wroclaw, Poland.
authors.forename: Wiktor
authors.identifier: 0000-0002-4642-1228
authors.initials: W
authors.lastname: Ejsmont
mesh_terms: D000465:Algorithms; D008432:Mathematical Computing; D008433:Mathematics / Q000379:methods*; D008962:Models, Theoretical; D011336:Probability; D015203:Reproducibility of Results