%I #13 Nov 23 2018 04:07:14
%S 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,
%T 1,34,100,156,128,92,52,1,1,66,278,526,534,373,170,94,1,1,130,796,
%U 1896,2546,2014,913,360,145,1,1,258,2318,7102,13074,12953,6796,2399,667,244
%N 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).
%H Seiichi Manyama, <a href="/A321876/b321876.txt">Antidiagonals n = 0..139, flattened</a>
%F G.f. of column k: Product_{i>=1, j>=1} 1/(1 - x^(i*j))^(j^k).
%F G.f. of column k: exp(Sum_{j>=1} sigma_(k+1)(j)*x^j/(j*(1 - x^j))).
%e Square array begins:
%e 1, 1, 1, 1, 1, 1, ...
%e 1, 1, 1, 1, 1, 1, ...
%e 3, 4, 6, 10, 18, 34, ...
%e 5, 8, 16, 38, 100, 278, ...
%e 11, 21, 52, 156, 526, 1896, ...
%e 17, 39, 128, 534, 2546, 13074, ...
%t 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
%t 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
%Y Columns k=0..9 give A006171, A061256, A275585, A288391, A301542, A301543, A301544, A301545, A301546, A301547.
%Y Main diagonal gives A319647.
%Y Cf. A321877.
%K nonn,tabl
%O 0,6
%A _Ilya Gutkovskiy_, Nov 20 2018