Geodesic
Finite prefix codes and finatary trees
The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 3, pp. 38-47

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We find an explicit formula for the number of all $p$-ary $k$-trees with $m$ leaves. Analyzing this formula, we arrive at a number of combinatorial identities.
Keywords: tree; prefix code; generating function; Fuss number; Catalan number; Motzkin language. 
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     title = {Finite prefix codes and finatary trees},
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I. O. Koryakov. Finite prefix codes and finatary trees. The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 3, pp. 38-47. http://geodesic.mathdoc.fr/item/IIGUM_2013_6_3_a2/