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

0,13

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, ... .

Links

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

Example

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, ...

Crossrefs

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

Main diagonal gives A000041.

Sequence in context: A261627 A237112 A238013 * A280134 A351256 A143488

Adjacent sequences: A303937 A303938 A303939 * A303941 A303942 A303943

Keyword

nonn,tabl

Author

Seiichi Manyama, May 03 2018

Status

approved