OFFSET
0,4
COMMENTS
As square array, it is A x B where A = square array A039599 (completed with zeros) and B = transpose of A. - Philippe Deléham, May 22 2015
FORMULA
T(n,k) = A000108(n). - R. J. Mathar, Nov 03 2016
G.f.: (x*C(x)-x*y*C(x*y))/(x-x*y), where C(x) is the g.f. of A000108. - Vladimir Kruchinin, Nov 19 2020
Sum_{n>=0} 1/a(n) = 4 + 28*Pi/(27*sqrt(3)). - Amiram Eldar, Aug 18 2022
EXAMPLE
Triangle begins:
1;
1, 1;
2, 2, 2;
5, 5, 5, 5 ;
14, 14, 14, 14, 14;
42, 42, 42, 42, 42, 42;
From Philippe Deléham, May 22 2015: (Start)
A = square array A039599, completed with zeros.
1.....0.....0.....0...
1.....1.....0.....0...
2.....3.....1.....0...
5.....9.....5.....1...
......................
B = transpose of A.
1.....1.....2.....5...
0.....1.....3.....9...
0.....0.....1.....5...
0.....0.....0.....1...
......................
A x B = this sequence read as square array.
1.....1.....2.....5...
1.....2.....5....14...
2.....5....14....42...
5....14....42...132...
...................... (End)
MATHEMATICA
Table[PadRight[{}, n + 1, CatalanNumber[n]], {n, 0, 8}] // Flatten (* Amiram Eldar, Aug 18 2022, after Harvey P. Dale at A172417 *)
PROG
(Python)
from math import isqrt
from sympy import catalan
def A168256(n): return catalan((isqrt(n+1<<3)+1>>1)-1) # Chai Wah Wu, Nov 04 2024
CROSSREFS
KEYWORD
AUTHOR
Mark Dols, Nov 21 2009
STATUS
approved