A131427 A000108(n) preceded by n zeros.

1, 0, 1, 0, 0, 2, 0, 0, 0, 5, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, 0, 0, 429, 0, 0, 0, 0, 0, 0, 0, 0, 1430, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4862, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16796, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58786, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 208012

Offset: 0

Author

Gary W. Adamson, Jul 10 2007

Keywords

• nonn
• tabl

Comments

Triangle given by A000004 DELTA A000012 where DELTA is the operator defined in A084938. - Philippe Deléham, Jul 12 2007

T(n,k) is the number of Dyck paths of semilength n having exactly k U=(1,1) steps. - Alois P. Heinz, Jun 09 2014

Examples

			First few rows of the triangle are:
1;
0, 1;
0, 0, 2;
0, 0, 0, 5;
0, 0, 0, 0, 14;
0, 0, 0, 0, 0, 42;
...
		

Links

• Alois P. Heinz, Rows n = 0..140, flattened

Crossrefs

Cf. A131428, A131429, A000108, A243752.

Programs

Maple

T:= (n, k)-> `if`(kAlois P. Heinz, Jun 09 2014

Mathematica

T[n_, n_] := CatalanNumber[n]; T[, ] = 0;
Table[T[n, k], {n, 0, 15}, {k, 0, n}] // Flatten (* Jean-François Alcover, May 20 2016 *)

Formula

A000108(n) preceded by n zeros, as an infinite lower triangular matrix.

Extensions

More terms from Philippe Deléham, Oct 16 2008