A369589 Triangular array read by rows: T(m,n) = number of Yamanouchi words over the alphabet {1, 2, ..., n} of length m that start with n, m >= 1, n = 1..m.

1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 4, 5, 3, 1, 1, 10, 14, 11, 4, 1, 1, 15, 35, 31, 19, 5, 1, 1, 35, 90, 106, 69, 29, 6, 1, 1, 56, 245, 323, 265, 127, 41, 7, 1, 1, 126, 644, 1093, 971, 583, 209, 55, 8, 1, 1, 210, 1716, 3439, 3644, 2446, 1106, 319, 71, 9, 1, 1, 462, 4707, 11716, 13771, 10616, 5323, 1904, 461, 89, 10, 1

Offset: 1

Author

Max Alekseyev, Jan 26 2024

Keywords

• nonn
• tabl

Examples

			Array starts with
  m=1: 1
  m=2: 1,  1
  m=3: 1,  1,  1
  m=4: 1,  3,  2,  1
  m=5: 1,  4,  5,  3,  1
  m=6: 1, 10, 14, 11,  4, 1
  m=7: 1, 15, 35, 31, 19, 5, 1
		

Links

• Wikipedia, Lattice word.

Crossrefs

Row sums: A238728.

Columns: A000012 (n=1), A037952 (n=2), A369591 (n=3).

Cf. A001006, A369588.