Geodesic
On Generating Series of Coloured Planar Trees
Séminaire lotharingien de combinatoire, Tome 55 (2005-2007)
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We generalize and reprove an identity of Parker and Loday. It states that certain pairs of generating series associated to coloured plane rooted trees are mutually reciprocal series. 

@article{SLC_2005-2007_55_a4,
     author = {Roland Bacher and Gilles Schaeffer},
     title = {On {Generating} {Series} of {Coloured} {Planar} {Trees}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2005-2007},
     volume = {55},
     url = {http://geodesic.mathdoc.fr/item/SLC_2005-2007_55_a4/}
}
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AU  - Gilles Schaeffer
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VL  - 55
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%J Séminaire lotharingien de combinatoire
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Roland Bacher; Gilles Schaeffer. On Generating Series of Coloured Planar Trees. Séminaire lotharingien de combinatoire, Tome 55 (2005-2007). http://geodesic.mathdoc.fr/item/SLC_2005-2007_55_a4/