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

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;
  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

Sequence in context: A325519 A221057 A094366 * A363193 A124018 A309288

Adjacent sequences: A341369 A341370 A341371 * A341373 A341374 A341375

Keyword

nonn,tabl,more

Author

Michel Marcus, Feb 10 2021

Status

approved