A118245 - OEIS

%I #5 Feb 13 2022 23:15:45

%S 1,1,1,1,2,1,1,4,4,1,1,7,11,7,1,11,25,25,11,1,1,16,51,74,51,16,1,1,22,

%T 96,191,191,96,22,1,1,29,169,441,602,441,169,29,1

%N Triangle generated from A001263 considered as a transform.

%C Each row of the triangle is a palindrome.

%F Let M be the Narayana (or Catalan) triangle, A001263 as an infinite lower triangular matrix. Generate an array by rows, taking the product (M * V); where V = rows of the Narayana triangle considered as vectors. Rows of the triangle are antidiagonals of the array.

%e First few rows of the array:

%e   1,  1,  1,   1,   1, ...

%e   1,  2,  4,   7,  11, ...

%e   1,  4, 11,  25,  51, ...

%e   1,  7, 25,  74, 191, ...

%e   1, 11, 51, 191, 602, ...

%e   ...

%e n-th row of the array is generated from (M * V), where V in turn = n-th row of the Narayana triangle: (1); (1, 1); (1, 3, 1); (1, 6, 6, 1); ... i.e., terms followed by zeros to form a vector, as (1, 3, 1, 0, 0, 0, ...). Example: T(6,3) and T(6,4) = 25 = 1*0 + 1*1 + 6*1 + 6*18 = 0+1+6+18 = 25.

%e First few rows of the triangle:

%e   1;

%e   1,  1;

%e   1,  2,  1;

%e   1,  4,  4,   1;

%e   1,  7, 11,   7,   1;

%e   1, 11, 25,  25,  11,  1;

%e   1, 16, 51,  74,  51, 16,  1;

%e   1, 22, 96, 191, 191, 96, 22, 1;

%e   ...

%Y Cf. A001263.

%K nonn,tabl

%O 1,5

%A _Gary W. Adamson_, Apr 17 2006