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