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Array of coefficients of characteristic polynomials of M_n, the n X n matrix with entries m_(i,j) = i mod j.
1

%I #8 Mar 30 2012 18:39:11

%S 1,-1,0,1,0,0,-1,0,2,0,1,0,-5,-2,0,-1,0,17,47,34,0,1,0,-30,-105,-72,

%T 36,0,-1,0,63,426,1143,1272,468,0,1,0,-103,-936,-3668,-7412,-8424,

%U -3744,0,-1,0,169,2104,11859,35084,55856,52680,33696,0,1,0,-250,-3883,-28047,-109953,-228920

%N Array of coefficients of characteristic polynomials of M_n, the n X n matrix with entries m_(i,j) = i mod j.

%e The characteristic polynomials of M_0, M_1, ..., M_4 are 1, -x + 0, x^2 + 0x + 0, -x^3 + 0x^2 + 2x + 0 and x^4 +0 x^3 - 5x^2 - 2x + 0, so the first 15 terms are 1; -1,0; 1,0,0; -1,0,2,0; 1,0,-5,-2,0.

%t c[0]={1}; c[n_] := Reverse[CoefficientList[CharacteristicPolynomial[Table[Mod[i, j], {i, 1, n}, {j, 1, n}], x], x]]; Flatten[c/@Range[0, 10]]

%K sign,tabl,easy

%O 0,9

%A _Benoit Cloitre_, Dec 15 2002