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

0,3

Links

Table of n, a(n) for n=0..53.

Example

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.

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}]]

Crossrefs

Cf. A231147.

Sequence in context: A274803 A274749 A247936 * A274858 A207997 A304489

Adjacent sequences: A231147 A231148 A231149 * A231151 A231152 A231153

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Nov 08 2013

Status

approved