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A321876
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1 - x^j)^sigma_k(j).
3
1, 1, 1, 1, 1, 3, 1, 1, 4, 5, 1, 1, 6, 8, 11, 1, 1, 10, 16, 21, 17, 1, 1, 18, 38, 52, 39, 34, 1, 1, 34, 100, 156, 128, 92, 52, 1, 1, 66, 278, 526, 534, 373, 170, 94, 1, 1, 130, 796, 1896, 2546, 2014, 913, 360, 145, 1, 1, 258, 2318, 7102, 13074, 12953, 6796, 2399, 667, 244
OFFSET
0,6
LINKS
FORMULA
G.f. of column k: Product_{i>=1, j>=1} 1/(1 - x^(i*j))^(j^k).
G.f. of column k: exp(Sum_{j>=1} sigma_(k+1)(j)*x^j/(j*(1 - x^j))).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, ...
3, 4, 6, 10, 18, 34, ...
5, 8, 16, 38, 100, 278, ...
11, 21, 52, 156, 526, 1896, ...
17, 39, 128, 534, 2546, 13074, ...
MATHEMATICA
Table[Function[k, SeriesCoefficient[Product[1/(1 - x^j)^DivisorSigma[k, j], {j, 1, n}], {x, 0, n}]][i - n], {i, 0, 10}, {n, 0, i}] // Flatten
Table[Function[k, SeriesCoefficient[Exp[Sum[DivisorSigma[k + 1, j] x^j/(j (1 - x^j)), {j, 1, n}]], {x, 0, n}]][i - n], {i, 0, 10}, {n, 0, i}] // Flatten
CROSSREFS
Main diagonal gives A319647.
Cf. A321877.
Sequence in context: A104730 A249488 A275204 * A131238 A133380 A343168
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Nov 20 2018
STATUS
approved