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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
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
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, May 03 2018
STATUS
approved

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Last modified March 28 04:05 EDT 2024. Contains 371235 sequences. (Running on oeis4.)