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Maximum modulus in the inverse of Hilbert's matrix.
5

%I #11 Feb 11 2020 12:03:23

%S 1,12,192,6480,179200,4410000,133402500,4249941696,122367445200,

%T 3480673996800,117643011932160,3659449159080000,106518477825760000,

%U 3521767173114190000,114708987924290760000,3525270042097046880000,110552468520163390156800

%N Maximum modulus in the inverse of Hilbert's matrix.

%C This sequence corrects A061065, which was wrong for n > 6. These values appear at the A210357(n) position on the diagonal. Thanks to Clark Kimberling for verifying this sequence.

%H T. D. Noe, <a href="/A210356/b210356.txt">Table of n, a(n) for n = 1..100</a>

%t Table[im = Inverse[HilbertMatrix[n]]; Max[Abs[Flatten[im]]]], {n, 20}]

%o (PARI) for(n=1,17, my(h=1/mathilbert(n),s=0); for(j=1,n, for(k=1,n, s=max(s,h[j,k]))); print1(s,", ")) \\ _Hugo Pfoertner_, Feb 11 2020

%Y Cf. A061065, A189765 (inverse matrix), A210357, A210358 (minimum).

%K nonn

%O 1,2

%A _T. D. Noe_, Mar 28 2012