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.

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

Offset: 1

Author

Clark Kimberling, Jan 08 2012

Keywords

• nonn
• tabl

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.

Examples

			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.
		

Crossrefs

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

Programs

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 *)