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A210357
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Location of the maximum modulus in the inverse of Hilbert's matrix.
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5
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1, 2, 2, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 24, 25, 26, 27, 27, 28, 29, 29, 30, 31, 31, 32, 33, 34, 34, 35, 36, 36, 37, 38, 39, 39, 40, 41, 41, 42, 43, 44, 44, 45, 46, 46, 47, 48, 48
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OFFSET
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1,2
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COMMENTS
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The maximum value always occurs on the diagonal. These numbers are close to n/sqrt(2).
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LINKS
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MATHEMATICA
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Table[im = Inverse[HilbertMatrix[n]]; pos = Position[im, Max[Abs[Flatten[im]]]]; If[Length[pos] > 1, Print[{n, pos}]; 0, pos[[1, 1]]], {n, 70}]
Table[t = Table[(2*i-1) Binomial[n+i-1, n-i]^2 * Binomial[2*i-2, i-1]^2, {i, n}]; Position[t, Max[t]][[1, 1]], {n, 100}]
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CROSSREFS
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Cf. A210356 (largest element in the inverse of Hilbert's matrix).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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