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A203904 Triangular array T; for n>0, row n shows the coefficients of a reduced polynomial having zeros -k/(n+1) for k=1,2,...,n. 2

%I #5 Mar 30 2012 18:58:07

%S 1,1,2,2,9,9,3,22,48,32,24,250,875,1250,625,10,137,675,1530,1620,648,

%T 720,12348,79576,252105,420175,352947,117649,315,6534,52528,216608,

%U 501760,659456,458752,131072,4480,109584,1063116,5450004,16365321

%N Triangular array T; for n>0, row n shows the coefficients of a reduced polynomial having zeros -k/(n+1) for k=1,2,...,n.

%C For n>0, the zeros of the polynomial represented by row n+1 interlace the zeros of the polynomial for row n; see the Example section.

%C ...

%C T(n,1): A119619

%C T(n,n): A056916.

%e First five rows(counting the top row as row 0):

%e 1

%e 1...2.................representing 1+2x

%e 1...9...9.............representing 2+9x+9x^2

%e 3...22..48...32

%e 24...250...875...1250...625

%e Zeros corresponding to rows 1 to 4:

%e .................-1/2

%e ............-2/3......-1/3

%e ......-3/4.......-1/2.......-1/4

%e -4/5........-3/5......-2/5.......-1/5

%e Interlace property for successive rows illustrated by

%e 1/5 < 1/4 < 2/5 < 1/2 < 3/5 < 3/4 < 4/5.

%t p[n_, x_] := Product[(n*x + k)/GCD[n, k], {k, 1, n - 1}]

%t Table[CoefficientList[p[n, x], x], {n, 1, 10}]

%t TableForm[%] (* A203904 triangle *)

%t Flatten[%%] (* A203904 sequence *)

%Y Cf. A056856, A119619, A056916, A007305/A007306 (Farey fractions).

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Jan 08 2012

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)