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Dyck Paths With No Peaks At Height k

2001
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Journal of Integer Sequences
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unpublished

A Dyck path of length 2n is a path in two-space from (0, 0) to (2n, 0) which uses only steps (1, 1) (north-east) and (1, −1) (south-east). Further, a Dyck path does not go below the x-axis. A peak on a Dyck path is a node that is immediately preceded by a northeast step and immediately followed by a southeast step. A peak is at height k if its y-coordinate is k. Let G k (x) be the generating function for the number of Dyck paths of length 2n with no peaks at height k with k ≥ 1. It is known

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