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Generating functions for the area below some lattice paths

Abstract : We study some lattice paths related to the concept ofgenerating trees. When the matrix associated to this kind of trees is a Riordan array $D=(d(t),h(t))$, we are able to find the generating function for the total area below these paths expressed in terms of the functions $d(t)$ and $h(t)$.
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Donatella Merlini. Generating functions for the area below some lattice paths. Discrete Random Walks, DRW'03, 2003, Paris, France. pp.217-228, ⟨10.46298/dmtcs.3323⟩. ⟨hal-01183918⟩

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