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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.

%I A203904 #5 Mar 30 2012 18:58:07
%S A203904 1,1,2,2,9,9,3,22,48,32,24,250,875,1250,625,10,137,675,1530,1620,648,
%T A203904 720,12348,79576,252105,420175,352947,117649,315,6534,52528,216608,
%U A203904 501760,659456,458752,131072,4480,109584,1063116,5450004,16365321
%N 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.
%C A203904 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 A203904 ...
%C A203904 T(n,1):  A119619
%C A203904 T(n,n):  A056916.
%e A203904 First five rows(counting the top row as row 0):
%e A203904 1
%e A203904 1...2.................representing 1+2x
%e A203904 1...9...9.............representing 2+9x+9x^2
%e A203904 3...22..48...32
%e A203904 24...250...875...1250...625
%e A203904 Zeros corresponding to rows 1 to 4:
%e A203904 .................-1/2
%e A203904 ............-2/3......-1/3
%e A203904 ......-3/4.......-1/2.......-1/4
%e A203904 -4/5........-3/5......-2/5.......-1/5
%e A203904 Interlace property for successive rows illustrated by
%e A203904   1/5 < 1/4 < 2/5 < 1/2 < 3/5 < 3/4 < 4/5.
%t A203904 p[n_, x_] := Product[(n*x + k)/GCD[n, k], {k, 1, n - 1}]
%t A203904 Table[CoefficientList[p[n, x], x], {n, 1, 10}]
%t A203904 TableForm[%]  (* A203904 triangle *)
%t A203904 Flatten[%%]   (* A203904 sequence *)
%Y A203904 Cf. A056856, A119619, A056916, A007305/A007306 (Farey fractions).
%K A203904 nonn,tabl
%O A203904 1,3
%A A203904 _Clark Kimberling_, Jan 08 2012