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A136160 Triangle T(n,k) = k*A053120(n,k).

%I A136160 #11 Sep 18 2017 10:27:41
%S A136160 1,0,4,-3,0,12,0,-16,0,32,5,0,-60,0,80,0,36,0,-192,0,192,-7,0,168,0,
%T A136160 -560,0,448,0,-64,0,640,0,-1536,0,1024,9,0,-360,0,2160,0,-4032,0,2304,
%U A136160 0,100,0,-1600,0,6720,0,-10240,0,5120,-11,0,660,0,-6160,0,19712,0,-25344,0,11264
%N A136160 Triangle T(n,k) = k*A053120(n,k).
%C A136160 The definition is equivalent to building the derivatives of the Chebyshev polynomials T(n,x) and listing the coefficients [x^k] dT/dx in row n.
%C A136160 Row sums are the squares A000079(n-1).
%C A136160 Obtained from A136265 by sign flips and nulling each second diagonal. - R. J. Mathar, Sep 04 2011
%D A136160 Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986, page 8 and pages 42 - 43
%H A136160 Peter Steinbach, <a href="http://www.jstor.org/stable/2691048">Golden fields: a case for the heptagon</a>, Math. Mag. Vol. 70, No. 1, Feb. 1997, 22-31.
%e A136160 1;
%e A136160 0, 4;
%e A136160 -3, 0, 12;
%e A136160 0, -16, 0, 32;
%e A136160 5, 0, -60, 0, 80;
%e A136160 0, 36, 0, -192, 0, 192;
%e A136160 -7, 0, 168, 0, -560, 0, 448;
%e A136160 0, -64, 0, 640, 0, -1536,0, 1024;
%e A136160 9, 0, -360, 0, 2160,0, -4032, 0, 2304;
%e A136160 0, 100, 0, -1600, 0, 6720, 0, -10240, 0, 5120;
%e A136160 -11, 0, 660, 0, -6160, 0, 19712, 0, -25344, 0, 11264;
%t A136160 P[x, 0] = 1; P[x, 1] = x; P[x_, n_] := P[x, n] = 2*x*P[x, n - 1] - P[x, n - 2]; Q[x_, n_] := D[P[x, n + 1], x]; a = Table[CoefficientList[Q[x, n], x], {n, 0, 10}]; Flatten[a]
%Y A136160 Cf. A053120, A135929.
%K A136160 uned,tabl,sign
%O A136160 1,3
%A A136160 _Roger L. Bagula_, Mar 16 2008