|
|
A302233
|
|
Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1 + x^(k*j))/(1 + x^j).
|
|
0
|
|
|
1, 1, 0, 1, -1, 0, 1, -1, 1, 0, 1, -1, 0, -2, 0, 1, -1, 0, 0, 2, 0, 1, -1, 0, -1, 0, -3, 0, 1, -1, 0, -1, 2, -1, 4, 0, 1, -1, 0, -1, 1, -2, 1, -5, 0, 1, -1, 0, -1, 1, 0, 1, -1, 6, 0, 1, -1, 0, -1, 1, -1, 0, -2, 1, -8, 0, 1, -1, 0, -1, 1, -1, 2, -1, 4, 0, 10, 0, 1, -1, 0, -1, 1, -1, 1, -2, 1, -4, 0, -12, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,14
|
|
LINKS
|
|
|
FORMULA
|
G.f. of column k: Product_{j>=1} (1 + x^(k*j))/(1 + x^j).
|
|
EXAMPLE
|
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, -1, -1, -1, -1, -1, ...
0, 1, 0, 0, 0, 0, ...
0, -2, 0, -1, -1, -1, ...
0, 2, 0, 2, 1, 1, ...
0, -3, -1, -2, 0, -1, ...
|
|
MATHEMATICA
|
Table[Function[k, SeriesCoefficient[Product[(1 + x^(k i))/(1 + x^i), {i, 1, n}], {x, 0, n}]][j - n + 1], {j, 0, 12}, {n, 0, j}] // Flatten
Table[Function[k, SeriesCoefficient[QPochhammer[-1, x^k]/QPochhammer[-1, x], {x, 0, n}]][j - n + 1], {j, 0, 12}, {n, 0, j}] // Flatten
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|