OFFSET
0,8
COMMENTS
A(n,k) is the number of partitions of n into distinct parts of k sorts: the parts are unordered, but not the sorts.
LINKS
FORMULA
G.f. of column k: Product_{j>=1} (1 + k*x^j).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 1, 2, 3, 4, 5, ...
0, 2, 6, 12, 20, 30, ...
0, 2, 6, 12, 20, 30, ...
0, 3, 10, 21, 36, 55, ...
MATHEMATICA
Table[Function[k, SeriesCoefficient[Product[(1 + k x^i), {i, 1, Infinity}], {x, 0, n}]][j - n], {j, 0, 12}, {n, 0, j}] // Flatten
Table[Function[k, SeriesCoefficient[QPochhammer[-k, x]/(1 + k), {x, 0, n}]][j - n], {j, 0, 12}, {n, 0, j}] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, May 17 2017
STATUS
approved