A303940 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-x^(j*(j+k)))/(1-x^j). in powers of x.

1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 3, 2, 1, 1, 2, 3, 4, 4, 3, 1, 1, 2, 3, 4, 5, 5, 3, 1, 1, 2, 3, 5, 6, 8, 7, 5, 1, 1, 2, 3, 5, 6, 9, 10, 10, 5, 1, 1, 2, 3, 5, 7, 10, 12, 14, 13, 8, 1, 1, 2, 3, 5, 7, 10, 13, 17, 18, 17, 9, 1, 1, 2, 3, 5, 7, 11, 14, 19, 23, 25, 22, 13

Offset: 0

Author

Seiichi Manyama, May 03 2018

Keywords

• nonn
• tabl

Comments

A(n,k) is the number of partitions of n into at most 0+k copies of 1, 1+k copies of 2, 2+k copies of 3, ... .

Examples

			Square array begins:
   1, 1, 1, 1,  1,  1,  1,  1, ...
   0, 1, 1, 1,  1,  1,  1,  1, ...
   1, 1, 2, 2,  2,  2,  2,  2, ...
   1, 2, 2, 3,  3,  3,  3,  3, ...
   1, 3, 4, 4,  5,  5,  5,  5, ...
   2, 4, 5, 6,  6,  7,  7,  7, ...
   3, 5, 8, 9, 10, 10, 11, 11, ...
		

Links

• Seiichi Manyama, Antidiagonals n = 0..139, flattened

Crossrefs

Columns k=0..2 give A087153, A052335, A303939.

Main diagonal gives A000041.