A318945 Triangle read by rows: T(n,k) (n>=2, 0 <= k <= n-2) = number of Dyck paths with k valleys of altitude k.

1, 4, 1, 13, 5, 1, 39, 19, 6, 1, 112, 64, 26, 7, 1, 313, 201, 97, 34, 8, 1, 859, 603, 331, 139, 43, 9, 1, 2328, 1752, 1064, 512, 191, 53, 10, 1

Offset

2,2

Links

Table of n, a(n) for n=2..37.

Czabarka, É., Flórez, R., Junes, L., & Ramírez, J. L., Enumerations of peaks and valleys on non-decreasing Dyck paths, Discrete Mathematics (2018), 341(10), 2789-2807.

Example

Triangle begins:
1,
4,1,
13,5,1,
39,19,6,1,
112,64,26,7,1,
313,201,97,34,8,1,
859,603,331,139,43,9,1,
2328,1752,1064,512,191,53,10,1,
...

Crossrefs

Columns 0, 1, 2. 3 are A105693, A318946, A318947, A319405.

Sequence in context: A324186 A357216 A055252 * A193956 A193843 A116414

Adjacent sequences: A318942 A318943 A318944 * A318946 A318947 A318948

Keyword

nonn,tabl,more

Author

N. J. A. Sloane, Sep 18 2018

Status

approved