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 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. 10
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 LINKS Table of n, a(n) for n=1..78. Index entries for sequences mentioned by Glaisher 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)). EXAMPLE 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, ... 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 CROSSREFS Columns k=0..12 give A002654, A050457, A002173, A050459, A050456, A321821, A321822, A321823, A321824, A321825, A321826, A321827, A321828. Cf. A109974, A322081, A322082, A322083, A322084. Sequence in context: A329042 A171660 A157117 * A264081 A061538 A123602 Adjacent sequences: A322140 A322141 A322142 * A322144 A322145 A322146 KEYWORD sign,tabl AUTHOR Ilya Gutkovskiy, Nov 28 2018 STATUS approved

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Last modified September 12 20:35 EDT 2024. Contains 375854 sequences. (Running on oeis4.)