A161564 Convolution triangle for A000293 (solid partitions): A000041 * A002836.

1, 0, 1, 2, 0, 2, 5, 2, 0, 3, 12, 5, 4, 0, 5, 24, 12, 10, 6, 0, 7, 56, 24, 24, 15, 10, 0, 11, 113, 56, 48, 36, 25, 14, 0, 15, 248, 113, 112, 72, 60, 35, 22, 0, 22, 503, 248, 226, 168, 120, 84, 55, 30, 0, 30

Offset: 0

Author

Gary W. Adamson, Jun 13 2009

Keywords

• nonn
• tabl

Comments

Row sums = A000293, solid partitions: (1, 1, 4, 10, 26, 59, 140, 307, 684,...)

Examples

			First few rows of the triangle =
1;
0, 1;
2, 0, 2;
5, 2, 0, 3;
12, 5, 4, 0, 5;
24, 12, 10, 6, 0, 7;
56, 24, 24, 15, 10, 0, 11;
113, 56, 48, 36, 25, 14, 0, 15;
248, 113, 112, 72, 60, 35, 22, 0, 22;
503, 248, 226, 168, 120, 84, 55, 30, 0, 30;
...
Example: row 4 = (12, 5, 4, 0, 5), sum = 26 = A000293(4).
		

Crossrefs

Cf. A000293, A000041, A002836

Formula

Triangle read by rows, A000041 convolved with A002836: (1, 0, 2, 5, 12, 24, 56,...). Antidiagonals of a convolution array, A002836 * A000041: 1, . 1, . 2, . 3, . 5, . 7, . 11,... 0, . 0, . 0, . 0, . 0, . 0, .. 0,... 2, . 2, . 4, . 6, .10, .14, ..22,... 5, . 5, . 10, .15, .25, .35, ..55,... 12 .12, . 24, .36, .60, .84, .132,... ...