A combinatorial interpretation of the Catalan transform of the Catalan numbers

Details A combinatorial interpretation of the Catalan transform of the Catalan numbers A combinatorial interpretation of the Catalan transform of the Catalan numbers

2011-11-03

arxiv.org/abs/1111.0996v2

Mathematics

Combinatorics

5 pages, added reference

Scientific paper

The Catalan transform of a sequence (a_{n})_{n>=0} is the sequence
(b_{n})_{n>=0} with b_{n} = Sum[k/(2n-k) (2n-k)-choose-(n-k) a_{k},k=0..n].
Here we show that the Catalan transform of the Catalan numbers has a simple
interpretation: it counts functions f:[1,n] -> [1,n] satisfying the condition
that, for all i

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