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In this note we investigate the generating series of the Eulercharacteristics of Hilbert scheme of points on cyclic quotient singularities oftype (p,1). We link the appearing combinatorics to p-fountains, ageneralization of the notion of fountain of coins. We obtain a representationof the generating series as coefficient of a two variable generating series.

Hilbert scheme of points on cyclic quotient singularities of type (p,1)