A341372 - OEIS

%I #4 Feb 10 2021 13:52:55

%S 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,

%T 67,83,74,27,8,2,4,17,119,162,212,92,44,11,1

%N 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.

%C See the link for a description of the gamma permutation.

%H Marilena Barnabei, Flavio Bonetti, Niccolò Castronuovo, and Robert Cori, <a href="https://doi.org/10.1016/j.tcs.2016.05.007">Some permutations on Dyck words</a>, Theoretical Computer Science, Volume 635, 4 July 2016, Pages 51-63.

%e Triangle begins:

%e   2;

%e   2,  1;

%e   3,  2,   1;

%e   3,  4,   4,   1;

%e   4,  5,  11,   4,   1;

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

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

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

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

%e   ...

%K nonn,tabl,more

%O 2,1

%A _Michel Marcus_, Feb 10 2021