OFFSET
1,5
COMMENTS
Create an array in which the n-th row (n >= 1) is the INVERT transform of the first n terms of A000108: (1, 1, 2, 5, 14,...) followed by zeros. For example, row 3 of the array is the INVERT transform of (1, 1, 2, 0, 0, 0,...). The array is:
1,...1,...1,...1,...1,...1,...
1,...2,...3,...5,...8,..13,...
1,...2,...5,...9,..18,..37,...
1,...2,...5,..14,..28,..62,...
...
Then the rows of the triangle are first differences of the COLUMNS of this array.
Row sums = the Catalan sequence A000108 starting with offset 1. Right border = the Catalan sequence.
EXAMPLE
First few rows of the triangle are:
1;
1, 1;
1, 2, 2;
1, 4, 4, 5;
1, 7, 10, 10, 14;
1, 12, 24, 25, 28, 42;
1, 20, 52, 70, 70, 84, 132;
1, 33, 112, 185, 196, 210, 264, 429;
1, 54, 238, 445, 588, 588, 660, 858, 1430;
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jun 25 2012
EXTENSIONS
Edited by N. J. A. Sloane, Jul 03 2012
STATUS
approved