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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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 A143488 A201159

Adjacent sequences:  A303937 A303938 A303939 * A303941 A303942 A303943

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, May 03 2018

STATUS

approved

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Last modified July 31 12:29 EDT 2021. Contains 346373 sequences. (Running on oeis4.)