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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).

%I A273168 #12 Jun 23 2016 00:03:03
%S A273168 1,2,2,8,2,8,16,32,16,32,128,16,32,16,128,256,256,64,512,256,512,1024,
%T A273168 256,2048,512,1024,512,2048,2048,8192,4096,8192,2048,8192,4096,8192,
%U A273168 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
%N 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).
%C A273168 The numerator sequence is given in A273167, where details are given.
%H A273168 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%F A273168 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.
%e A273168 The triangle a(n, m) begins:
%e A273168 n\m     0    1    2    3    4    5    6    7
%e A273168 0:      1
%e A273168 1:      2    2
%e A273168 2:      8    2    8
%e A273168 3:     16   32   16   32
%e A273168 4:    128   16   32   16  128
%e A273168 5:    256  256   64  512  256  512
%e A273168 6:   1024  256 2048  512 1024  512 2048
%e A273168 7:   2048 8192 4096 8192 2048 8192 4096 8192
%e A273168 ...
%e A273168 row 8: 32768 2048 4096 2048 8192 2048 4096 2048 32768,
%e A273168 row 9: 65536 65536 8192 32768 16384 32768 8192 131072 65536 131072,
%e A273168 ...
%o A273168 (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)));
%o A273168 tabl(nn) = for (n=0, nn, for (k=0, n, print1(a(n,k), ", ")); print()); \\ _Michel Marcus_, Jun 19 2016
%Y A273168 Cf. A273167.
%K A273168 nonn,tabl,frac,easy
%O A273168 0,2
%A A273168 _Wolfdieter Lang_, Jun 12 2016