A273168 Denominators of coefficient triangle for expansion of x^(2*n) in terms of Chebyshev polynomials of the first kind T(2*m, x) (A127674).

1, 2, 2, 8, 2, 8, 16, 32, 16, 32, 128, 16, 32, 16, 128, 256, 256, 64, 512, 256, 512, 1024, 256, 2048, 512, 1024, 512, 2048, 2048, 8192, 4096, 8192, 2048, 8192, 4096, 8192, 32768, 2048, 4096, 2048, 8192, 2048, 4096, 2048, 32768, 65536, 65536, 8192, 32768, 16384, 32768, 8192, 131072, 65536, 131072, 262144, 65536, 262144, 32768, 65536, 32768, 524288, 131072, 262144, 131072, 524288

Offset

0,2

Comments

The numerator sequence is given in A273167, where details are given.

Links

Table of n, a(n) for n=0..65.

Index entries for sequences related to Chebyshev polynomials.

Formula

a(n, m) = denominator(R(n, m)), n >= 0, m = 1, ..., n, with the rationals R(n, m) given by R(n, 0) = (1/2^(2*n-1)) * binomial(2*n,n)/2 and R(n ,m) = (1/2^(2*n-1))*binomial(2*n, n-m) for m =1..n, n >= 0.

Example

The triangle a(n, m) begins:
n\m     0    1    2    3    4    5    6    7
0:      1
1:      2    2
2:      8    2    8
3:     16   32   16   32
4:    128   16   32   16  128
5:    256  256   64  512  256  512
6:   1024  256 2048  512 1024  512 2048
7:   2048 8192 4096 8192 2048 8192 4096 8192
...
row 8: 32768 2048 4096 2048 8192 2048 4096 2048 32768,
row 9: 65536 65536 8192 32768 16384 32768 8192 131072 65536 131072,
...

Prog

(PARI) a(n, m) = if (m == 0, denominator((1/2^(2*n-1)) * binomial(2*n, n)/2), denominator((1/2^(2*n-1))*binomial(2*n, n-m)));
tabl(nn) = for (n=0, nn, for (k=0, n, print1(a(n, k), ", ")); print()); \\ Michel Marcus, Jun 19 2016

Crossrefs

Cf. A273167.

Sequence in context: A342818 A174354 A011147 * A098818 A092694 A098984

Adjacent sequences: A273165 A273166 A273167 * A273169 A273170 A273171

Keyword

nonn,tabl,frac,easy

Author

Wolfdieter Lang, Jun 12 2016

Status

approved