A131303 2*A122204(deleting the right border of zeros) - A000012.
1, 3, 1, 5, 5, 1, 7, 3, 3, 1, 9, 15, 5, 3, 1, 11, 13, 7, 5, 3, 1, 13, 11, 11, 9, 5, 3, 115, 7, 9, 7, 9, 5, 3, 1, 17, 9, 13, 11, 11, 11, 5, 3, 1, 19, 43, 15, 13, 7, 7, 7, 5, 3, 1
Offset: 1
Examples
First few rows of the triangle: 1; 3, 1; 5, 5, 1; 7, 3, 3, 1; 9, 15, 5, 3, 1; 11, 13, 7, 5, 3, 1; 13, 11, 11, 9, 5, 3, 1; ...