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A333925
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j=2..k+1} 1/(1 - x^j).
1
1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 2, 1, 1, 0, 1, 0, 1, 1, 2, 1, 2, 0, 0, 1, 0, 1, 1, 2, 2, 3, 1, 1, 0, 1, 0, 1, 1, 2, 2, 3, 2, 2, 0, 0, 1, 0, 1, 1, 2, 2, 4, 3, 4, 2, 1, 0, 1, 0, 1, 1, 2, 2, 4, 3, 5, 3, 2, 0, 0, 1, 0, 1, 1, 2, 2, 4, 4, 6, 5, 5, 2, 1, 0
OFFSET
0,33
COMMENTS
A(n,k) is the number of partitions of n into parts 2, 3, ..., k and k + 1.
LINKS
David A. Corneth, Table of n, a(n) for n = 0..10010 (first 141 rows antidiagonals flattened)
FORMULA
G.f. of column k: Product_{j=2..k+1} 1/(1 - x^j).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 0, 0, 0, 0, 0, ...
0, 1, 1, 1, 1, 1, ...
0, 0, 1, 1, 1, 1, ...
0, 1, 1, 2, 2, 2, ...
0, 0, 1, 1, 2, 2, ...
MATHEMATICA
Table[Function[k, SeriesCoefficient[Product[1/(1 - x^j), {j, 2, k + 1}], {x, 0, n}]][i - n], {i, 0, 13}, {n, 0, i}] // Flatten
CROSSREFS
Main diagonal gives A002865.
Sequence in context: A194821 A044934 A124761 * A342595 A156709 A081400
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Apr 10 2020
STATUS
approved