A153585 Convolution triangle, A053121 * (A001405 * 0^(n-k)).

1, 0, 1, 1, 0, 2, 0, 2, 0, 3, 2, 0, 6, 0, 6, 0, 5, 0, 12, 0, 10, 5, 0, 18, 0, 30, 0, 20, 0, 14, 0, 42, 0, 60, 0, 35, 14, 0, 56, 0, 120, 0, 140, 0, 70, 0, 42, 0, 144, 0, 270, 0, 280, 0, 126

Offset: 0

Author

Gary W. Adamson, Dec 28 2008

Keywords

• nonn
• tabl

Comments

Row sums = A145974: (1, 1, 3, 5, 14, 27, 73,...).

Examples

			First few rows of the triangle =
1;
0, 1;
1, 0, 2;
0, 2, 0, 3;
2, 0, 6, 0, 6;
0, 5, 0, 12, 0, 10;
5, 0, 18, 0, 30, 0, 20;
0, 14, 0, 42, 0, 60, 0, 35;
14, 0, 56, 0, 120, 0, 140, 0, 70;
0, 42, 0, 144, 0, 270, 0, 280, 0, 126;
42, 0, 180, 0, 450, 0, 700, 0, 630, 0, 252;
...
Example: Row 4 = (2, 0, 6, 0, 6) = termwise products of (2, 0, 3, 0, 1) and (1, 1, 2, 3, 6).
		

Formula

Convolution triangle, A053121 * (A001405 * 0^(n-k)).

A053121 = the aerated Catalan triangle and (A001405 * 0^(n-k) = an

infinite lower triangular matrix with A001405 as the main diagonal and

the rest zeros.