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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
1, 1, 2, 2, 9, 9, 3, 22, 48, 32, 24, 250, 875, 1250, 625, 10, 137, 675, 1530, 1620, 648, 720, 12348, 79576, 252105, 420175, 352947, 117649, 315, 6534, 52528, 216608, 501760, 659456, 458752, 131072, 4480, 109584, 1063116, 5450004, 16365321 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

...

T(n,1):  A119619

T(n,n):  A056916.

LINKS

Table of n, a(n) for n=1..41.

EXAMPLE

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

1

1...2.................representing 1+2x

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

3...22..48...32

24...250...875...1250...625

Zeros corresponding to rows 1 to 4:

.................-1/2

............-2/3......-1/3

......-3/4.......-1/2.......-1/4

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

Interlace property for successive rows illustrated by

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

MATHEMATICA

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

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

TableForm[%]  (* A203904 triangle *)

Flatten[%%]   (* A203904 sequence *)

CROSSREFS

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

Sequence in context: A198423 A229116 A346918 * A104681 A056856 A133920

Adjacent sequences:  A203901 A203902 A203903 * A203905 A203906 A203907

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 08 2012

STATUS

approved

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Last modified October 24 18:08 EDT 2021. Contains 348233 sequences. (Running on oeis4.)