A341372 - OEIS

A341372

Regular triangle read by rows, T(n, k) is the number of cycles of length 2*k-1 of the permutation gamma on Dn, the set of Dyck words of length n, for n>=2 and 1<=k<=n-1.

2, 2, 1, 3, 2, 1, 3, 4, 4, 1, 4, 5, 11, 4, 1, 2, 10, 21, 14, 6, 1, 6, 10, 44, 34, 24, 6, 1, 5, 17, 67, 83, 74, 27, 8, 2, 4, 17, 119, 162, 212, 92, 44, 11, 1

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OFFSET

2,1

COMMENTS

See the link for a description of the gamma permutation.

LINKS

Table of n, a(n) for n=2..46.

Marilena Barnabei, Flavio Bonetti, Niccolò Castronuovo, and Robert Cori, Some permutations on Dyck words, Theoretical Computer Science, Volume 635, 4 July 2016, Pages 51-63.

EXAMPLE

Triangle begins:

2, 1;

3, 2, 1;

3, 4, 4, 1;

4, 5, 11, 4, 1;

2, 10, 21, 14, 6, 1;

6, 10, 44, 34, 24, 6, 1;

5, 17, 67, 83, 74, 27, 8, 2;

4, 17, 119, 162, 212, 92, 44, 11, 1;

...

CROSSREFS