A231150 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.

1, 1, 2, 3, 2, 4, 9, 9, 4, 8, 24, 33, 24, 8, 16, 60, 105, 105, 60, 16, 32, 144, 306, 387, 306, 144, 32, 64, 336, 840, 1281, 1281, 840, 336, 64, 128, 768, 2208, 3936, 4737, 3936, 2208, 768, 128, 256, 1728, 5616, 11448, 16065, 16065, 11448, 5616, 1728, 256

Offset: 0

Author

Clark Kimberling, Nov 08 2013

Keywords

• nonn
• tabl
• easy

Examples

			First 6 rows:
1
1 .... 1
2 .... 3 ..... 2
4 .... 9 ..... 9 ...... 4
8 .... 24 .... 33 .... 24 .... 8
16 ... 60 .... 105 ... 105 ... 60 ... 16
The first 4 polynomials: 1, 1 + x, 2 + 3*x + 2*x^2, 4 + 9*x + 9*x^2 + 4*x^3.
		

Crossrefs

Cf. A231147.

Programs

Mathematica

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}]]