Geodesic
A partition of the Catalan numbers and enumeration of genealogical trees
Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 2, pp. 181-195

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A special relational structure, called genealogical tree, is introduced; its social interpretation and geometrical realizations are discussed. The numbers C_n,k of all abstract genealogical trees with exactly n+1 nodes and k leaves is found by means of enumeration of code words. For each n, the C_n,k form a partition of the n-th Catalan numer Cₙ, that means C_n,1+C_n,2+ ...+C_n,n = Cₙ.
Keywords: genealogical tree, Catalan number, generating function 
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Schimming, Rainer. A partition of the Catalan numbers and enumeration of genealogical trees. Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 2, pp. 181-195. http://geodesic.mathdoc.fr/item/DMGT_1996_16_2_a8/