A172417 Triangle read by rows: Catalan number C(n) repeated n times.

1, 2, 2, 5, 5, 5, 14, 14, 14, 14, 42, 42, 42, 42, 42, 132, 132, 132, 132, 132, 132, 429, 429, 429, 429, 429, 429, 429, 1430, 1430, 1430, 1430, 1430, 1430, 1430, 1430, 4862, 4862, 4862, 4862, 4862, 4862, 4862, 4862, 4862, 16796, 16796, 16796, 16796, 16796

Offset

1,2

Comments

Read as a square array, we obtain the Hankel matrix ( 1/(i+j)*binomial(2*i+2*j-2, i+j-1) )_i,j >= 1 equal to A039598 * transpose(A039598) (Cholesky factorization). See Chamberland, p. 1669. - Peter Bala, Oct 15 2023

Links

Table of n, a(n) for n=1..50.

Marc Chamberland, Factored matrices can generate combinatorial identities, Linear Algebra and its Applications, Volume 438, Issue 4, 2013, pp. 1667-1677.

Formula

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

Sum_{n>=1} 1/a(n) = 2 + 16*Pi/(27*sqrt(3)). - Amiram Eldar, Aug 18 2022

Example

Triangle begins:
.....1
....2,2
...5,5,5
14,14,14,14

Mathematica

Table[PadRight[{}, n, CatalanNumber[n]], {n, 10}]//Flatten (* Harvey P. Dale, Jun 05 2021 *)

Crossrefs

Cf. A001791 (row sums), A000108, A039598, A168256, A172414.

Sequence in context: A025510 A350172 A356387 * A158106 A185313 A208301

Adjacent sequences: A172414 A172415 A172416 * A172418 A172419 A172420

Keyword

nonn,tabl,easy,less

Author

Mark Dols, Feb 02 2010

Extensions

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

Status

approved