A322143 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = Sum_{d|n, d==1 (mod 4)} d^k - Sum_{d|n, d==3 (mod 4)} d^k.
1, 1, 1, 1, 1, 0, 1, 1, -2, 1, 1, 1, -8, 1, 2, 1, 1, -26, 1, 6, 0, 1, 1, -80, 1, 26, -2, 0, 1, 1, -242, 1, 126, -8, -6, 1, 1, 1, -728, 1, 626, -26, -48, 1, 1, 1, 1, -2186, 1, 3126, -80, -342, 1, 7, 2, 1, 1, -6560, 1, 15626, -242, -2400, 1, 73, 6, 0, 1, 1, -19682, 1, 78126, -728, -16806, 1, 703, 26, -10, 0
Offset: 1
Examples
Square array begins: 1, 1, 1, 1, 1, 1, ... 1, 1, 1, 1, 1, 1, ... 0, -2, -8, -26, -80, -242, ... 1, 1, 1, 1, 1, 1, ... 2, 6, 26, 126, 626, 3126, ... 0, -2, -8, -26, -80, -242, ...
Crossrefs
Programs
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Mathematica
Table[Function[k, SeriesCoefficient[Sum[(-1)^(j - 1) (2 j - 1)^k x^(2 j - 1)/(1 - x^(2 j - 1)), {j, 1, n}], {x, 0, n}]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten
Formula
G.f. of column k: Sum_{j>=1} (-1)^(j-1)*(2*j - 1)^k*x^(2*j-1)/(1 - x^(2*j-1)).