A172414 Triangle read by rows: Catalan number C(n) repeated 2*n+1 times.

1, 1, 1, 1, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 14, 14, 14, 14, 14, 14, 14, 14, 14, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 132, 132, 132, 132, 132, 132, 132, 132, 132, 132, 132, 132, 132, 429, 429, 429, 429, 429, 429, 429, 429, 429, 429, 429, 429, 429, 429, 429

Offset: 0

Author

Mark Dols, Feb 02 2010

Keywords

• nonn
• tabf
• easy
• less

Examples

			Triangle begins:
......1
....1,1,1
..2,2,2,2,2
5,5,5,5,5,5,5,
		

Crossrefs

Cf. A000108, A001700 (row sums), A172417, A168256.

Programs

Mathematica

Table[PadRight[{}, 2*n + 1, CatalanNumber[n]], {n, 0, 8}] // Flatten (* Amiram Eldar, Aug 18 2022, after Harvey P. Dale at A172417 *)

Formula

T(n,k) = A000108(n). - R. J. Mathar, Nov 03 2016

Sum_{n>=0} 1/a(n) = 6 + 44*Pi/(27*sqrt(3)). - Amiram Eldar, Aug 18 2022

Extensions

Offset corrected by R. J. Mathar, Nov 03 2016

Data corrected and extended by Amiram Eldar, Aug 18 2022