OFFSET
0,12
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
G.f. of column k: Product_{j>=1} (1 - x^j)/(1 - k*x^j).
G.f. of column k: exp(Sum_{j>=1} ( Sum_{d|j} d*(k^(j/d) - 1) ) * x^j/j).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
-1, 0, 1, 2, 3, 4, ...
-1, 0, 3, 8, 15, 24, ...
0, 0, 6, 24, 60, 120, ...
0, 0, 14, 78, 252, 620, ...
1, 0, 27, 232, 1005, 3096, ...
MATHEMATICA
Table[Function[k, SeriesCoefficient[Product[(1 - x^i)/(1 - k x^i), {i, n}], {x, 0, n}]][j - n], {j, 0, 11}, {n, 0, j}] // Flatten
Table[Function[k, SeriesCoefficient[Exp[Sum[Sum[d (k^(i/d) - 1), {d, Divisors[i]}] x^i/i, {i, n}]], {x, 0, n}]][j - n], {j, 0, 11}, {n, 0, j}] // Flatten
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Ilya Gutkovskiy, Sep 27 2018
STATUS
approved