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A347227
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Square array T(n,k), n >= 1, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{d|n} mu(d)*mu(n/d)*d^k.
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2
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1, 1, -2, 1, -3, -2, 1, -5, -4, 1, 1, -9, -10, 2, -2, 1, -17, -28, 4, -6, 4, 1, -33, -82, 8, -26, 12, -2, 1, -65, -244, 16, -126, 50, -8, 0, 1, -129, -730, 32, -626, 252, -50, 0, 1, 1, -257, -2188, 64, -3126, 1394, -344, 0, 3, 4, 1, -513, -6562, 128, -15626, 8052, -2402, 0, 9, 18, -2
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OFFSET
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1,3
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LINKS
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FORMULA
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Dirichlet g.f. of column k: 1/(zeta(s)*zeta(s-k)).
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, 1, ...
-2, -3, -5, -9, -17, -33, ...
-2, -4, -10, -28, -82, -244, ...
1, 2, 4, 8, 16, 32, ...
-2, -6, -26, -126, -626, -3126, ...
4, 12, 50, 252, 1394, 8052, ...
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MATHEMATICA
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T[n_, k_] := DivisorSum[n, MoebiusMu[#] * MoebiusMu[n/#] * #^k &]; Table[T[n - k + 1, k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* Amiram Eldar, Aug 24 2021 *)
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PROG
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(PARI) T(n, k) = sumdiv(n, d, moebius(d)*moebius(n/d)*d^k);
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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