A127373 Triangle, row sums = A023896, left column = A053570.
1, 1, 0, 2, 1, 0, 3, 0, 1, 0, 6, 2, 1, 1, 0, 5, 0, 0, 0, 1, 0, 12, 4, 2, 1, 1, 1, 0, 13, 0, 1, 0, 1, 0, 1, 0, 18, 4, 0, 2, 1, 0, 1, 1, 0, 15, 0, 3, 0, 0, 0, 1, 0, 1, 0
Offset: 1
Examples
First few rows of the triangle: 1; 1, 0; 2, 1, 0; 3, 0, 1, 0; 6, 2, 1, 1, 0; 5, 0, 0, 0, 1, 0 12, 4, 2, 1, 1, 1, 0; ...
Comments