A231150 - OEIS

%I #7 Nov 10 2013 14:19:07

%S 1,1,2,3,2,4,9,9,4,8,24,33,24,8,16,60,105,105,60,16,32,144,306,387,

%T 306,144,32,64,336,840,1281,1281,840,336,64,128,768,2208,3936,4737,

%U 3936,2208,768,128,256,1728,5616,11448,16065,16065,11448,5616,1728,256

%N Array of coefficients of numerator polynomials of the rational function p(n, x^(1/2)+x^(-1/2)), where p(n,x) is the n-th Chebyshev polynomial of the 1st kind.

%e First 6 rows:

%e 1

%e 1 .... 1

%e 2 .... 3 ..... 2

%e 4 .... 9 ..... 9 ...... 4

%e 8 .... 24 .... 33 .... 24 .... 8

%e 16 ... 60 .... 105 ... 105 ... 60 ... 16

%e The first 4 polynomials: 1, 1 + x, 2 + 3*x + 2*x^2, 4 + 9*x + 9*x^2 + 4*x^3.

%t z = 60; p[n_, x_] := p[n, x] = ChebyshevT[n, x]; f1[n_, x_] := f1[n, x] = Numerator[Factor[p[n, x] /. x -> Sqrt[x] + 1/Sqrt[x]]]; Table[Expand[f1[n, x]], {n, 0, z/4}]; t = Flatten[Table[CoefficientList[f1[n, x], x], {n, 1, z/4}]]

%Y Cf. A231147.

%K nonn,tabl,easy

%O 0,3

%A _Clark Kimberling_, Nov 08 2013