A168534 Triangle read by rows, A168532 * A000012; as infinite lower triangular matrices.

1, 2, 1, 3, 1, 1, 5, 2, 1, 1, 7, 1, 1, 1, 1, 11, 4, 2, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 22, 5, 2, 2, 1, 1, 1, 1, 30, 3, 3, 1, 1, 1, 1, 1, 1, 42, 8, 2, 2, 2, 1, 1, 1, 1, 1, 56, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 77, 14, 7, 4, 2, 2, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Gary W. Adamson, Nov 28 2009

Keywords

• nonn
• tabl

Comments

Row sums = A078392: (1, 3, 5, 9, 11, 20, 21,...).

Triangle A168533 = A000012 * A168532

Left border = the partition numbers, A000041 starting with offset 1.

Examples

			First few rows of the triangle =
1;
2, 1;
3, 1, 1;
5, 2, 1, 1;
7, 1, 1, 1, 1;
11, 4, 2, 1, 1, 1;
15, 1, 1, 1, 1, 1, 1;
22, 5, 2, 2, 1, 1, 1, 1;
30, 3, 3, 1, 1, 1, 1, 1, 1;
42, 8, 2, 2, 2, 1, 1, 1, 1, 1;
56, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
77, 14, 7, 4, 2, 2, 1, 1, 1, 1, 1, 1;
101, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
135, 16, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1;
176, 9, 9, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
231, 22, 5, 5, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1;
...
		

Crossrefs

Cf. A168532, A168533, A000041, A078392

Formula

Triangle read by rows, A168532 * A000012; where A000012 = an infinite lower

triangular matrix with all 1's. The operation takes partial row sums

starting from the right of each row.