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

0,5

Links

Table of n, a(n) for n=0..63.

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A215924 A115101 A241148 * A266995 A051887 A139516

Adjacent sequences: A172411 A172412 A172413 * A172415 A172416 A172417

Keyword

nonn,tabf,easy,less

Author

Mark Dols, Feb 02 2010

Extensions

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

Data corrected and extended by Amiram Eldar, Aug 18 2022

Status

approved