login
A137940
Triangle read by rows, antidiagonals of an array formed by A000012 * A001263 (transform).
2
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
1,5
COMMENTS
Rows of the array tend to the Catalan sequence, A000108 starting (1, 2, 5, 14, 42, ...).
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.
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.
EXAMPLE
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;
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Feb 24 2008
EXTENSIONS
More terms from Alois P. Heinz, Nov 28 2021
STATUS
approved