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%I #8 Feb 19 2015 17:10:15
%S 1,4,4,8,16,16,64,64,64,64,128,64,64,256,256,512,512,1024,1024,1024,
%T 1024,1024,4096,4096,2048,2048,4096,4096,16384,16384,16384,16384,
%U 16384,16384,16384,16384,32768,8192,8192,16384,16384,8192,8192,65536,65536,131072,131072,65536,65536,65536,65536,262144,262144,262144,262144,262144,524288,524288,131072,131072,1048576,1048576,524288,524288,1048576,1048576
%N Denominators of coefficient triangle for expansion of x^n in terms of polynomials Todd(k,x) = T(2*k+1, sqrt(x))/sqrt(x) (A084930), with the Chebyshev T-polynomials.
%C For the numerator triangle see A244420, also for comments, and the rational entries R(n,m) of the lower triangular Riordan matrix denoted in standard fashion by ((2 - c(z/4)/(1-z), -1 + c(z/4)) with c the o.g.f. of the Catalan numbers A000108.
%H Wolfdieter Lang, <a href="/A244421/a244421.pdf">First rows of the triangle.</a>
%F a(n,m) = denominator(R(n,m)) with the rationals Riordan matrix elements R(n,m)= [x^m]R(n,x), with the row polynomials R(n,x) generated by ((2 - c(z/4))/(1-z))/(1 - x*(-1 + c(z/4))) = 2*((1+x)*(z-1) + (1-x)*sqrt(1-z))/((1-z)*((1+x)^2*z - 4*x)), where c(x) is the o.g.f. of the Catalan numbers A000108.
%e The triangle a(n,m) begins:
%e n\m 0 1 2 3 4 5 6 ...
%e 0: 1
%e 1: 4 4
%e 2: 8 16 16
%e 3: 64 64 64 64
%e 4: 128 64 64 256 256
%e 5: 512 512 1024 1024 1024 1024
%e 6: 1024 4096 4096 2048 2048 4096 4096
%e ...
%e For more rows see the link.
%e For the rational triangle R(n,m) see the example section of A244420.
%e Expansion: x^3 = (35*Todd(0, x) + 21*Todd(1, x) + 7*Todd(2, x) + 1*Todd(3, x))/64 = (35 + 21*(-3+4*x) + 7*( 5-20*x+16*x^2) + (-7+56*x-112*x^2+64*x^3))/64. For the Todd polynomials see A084930.
%Y Cf. A084930, A244420, A000108.
%K nonn,easy,frac,tabl
%O 0,2
%A _Wolfdieter Lang_, Aug 04 2014
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