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A321877 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1 + x^j)^sigma_k(j).

%I A321877 #10 Nov 23 2018 04:06:23
%S A321877 1,1,1,1,1,2,1,1,3,4,1,1,5,7,6,1,1,9,15,14,10,1,1,17,37,41,28,17,1,1,
%T A321877 33,99,137,107,58,25,1,1,65,277,491,487,286,106,38,1,1,129,795,1829,
%U A321877 2429,1749,700,201,59,1,1,257,2317,6971,12763,12056,5901,1735,372,86
%N A321877 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1 + x^j)^sigma_k(j).
%H A321877 Seiichi Manyama, <a href="/A321877/b321877.txt">Antidiagonals n = 0..139, flattened</a>
%F A321877 G.f. of column k: Product_{i>=1, j>=1} (1 + x^(i*j))^(j^k).
%F A321877 G.f. of column k: exp(Sum_{j>=1} sigma_(k+1)(j)*x^j/(j*(1 - x^(2*j)))).
%e A321877 Square array begins:
%e A321877    1,   1,    1,    1,     1,      1,  ...
%e A321877    1,   1,    1,    1,     1,      1,  ...
%e A321877    2,   3,    5,    9,    17,     33,  ...
%e A321877    4,   7,   15,   37,    99,    277,  ...
%e A321877    6,  14,   41,  137,   491,   1829,  ...
%e A321877   10,  28,  107,  487,  2429,  12763,  ...
%t A321877 Table[Function[k, SeriesCoefficient[Product[(1 + x^j)^DivisorSigma[k, j], {j, 1, n}], {x, 0, n}]][i - n], {i, 0, 10}, {n, 0, i}] // Flatten
%t A321877 Table[Function[k, SeriesCoefficient[Exp[Sum[DivisorSigma[k + 1, j] x^j/(j (1 - x^(2 j))), {j, 1, n}]], {x, 0, n}]][i - n], {i, 0, 10}, {n, 0, i}] // Flatten
%Y A321877 Columns k=0..9 give A107742, A192065, A288414, A288415, A301548, A301549, A301550, A301551, A301552, A301553.
%Y A321877 Main diagonal gives A321042.
%Y A321877 Cf. A321876.
%K A321877 nonn,tabl
%O A321877 0,6
%A A321877 _Ilya Gutkovskiy_, Nov 20 2018