A137940 Triangle read by rows, antidiagonals of an array formed by A000012 * A001263 (transform).

1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 2, 5, 7, 1, 1, 2, 5, 13, 11, 1, 1, 2, 5, 14, 31, 16, 1, 1, 2, 5, 14, 41, 66, 22, 1, 1, 2, 5, 14, 42, 116, 127, 29, 1, 1, 2, 5, 14, 42, 131, 302, 225, 37, 1, 1, 2, 5, 14, 42, 132, 407, 715, 373, 46, 1, 1, 2, 5, 14, 42, 132, 428, 1205, 1549, 586, 56, 1

Offset: 1

Author

Gary W. Adamson, Feb 24 2008

Keywords

• nonn
• tabl

Comments

Rows of the array tend to the Catalan sequence, A000108 starting (1, 2, 5, 14, 42, ...).

Examples

			First few rows of the array:
  1, 1, 1,  1,  1, ...
  1, 2, 4,  7, 11, ...
  1, 2, 5, 13, 31, ...
  1, 2, 5, 14, 41, ...
  1, 2, 5, 14, 42, ...
  ...
First few rows of the triangle:
  1;
  1, 1;
  1, 2, 1;
  1, 2, 4,  1;
  1, 2, 5,  7,  1;
  1, 2, 5, 13, 11,   1;
  1, 2, 5, 14, 31,  16,   1;
  1, 2, 5, 14, 41,  66,  22,   1;
  1, 2, 5, 14, 42, 116, 127,  29,   1;
  1, 2, 5, 14, 42, 131, 302, 225,  37,  1;
  1, 2, 5, 14, 42, 132, 407, 715, 373, 46, 1;
  ...
		

Links

• Antonio Bernini, Matteo Cervetti, Luca Ferrari, Einar Steingrimsson, Enumerative combinatorics of intervals in the Dyck pattern poset, arXiv:1910.00299 [math.CO], 2019. See Table 1 p. 4.

Crossrefs

Cf. A001263, A000108, A106396.

Formula

Antidiagonals of an array formed by A000012 * A001263(transform), as infinite triangular matrices. A000012 = (1; 1,1; 1,1,1; 1,1,1,1; ...), A001263 = the Narayana triangle.

Extensions

More terms from Alois P. Heinz, Nov 28 2021