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A244421 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. 5
1, 4, 4, 8, 16, 16, 64, 64, 64, 64, 128, 64, 64, 256, 256, 512, 512, 1024, 1024, 1024, 1024, 1024, 4096, 4096, 2048, 2048, 4096, 4096, 16384, 16384, 16384, 16384, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

LINKS

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

Wolfdieter Lang, First rows of the triangle.

FORMULA

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.

EXAMPLE

The triangle  a(n,m) begins:

n\m   0     1     2     3     4     5     6 ...

0:    1

1:    4     4

2:    8    16    16

3:   64    64    64    64

4:  128    64    64   256   256

5:  512   512  1024  1024  1024  1024

6: 1024  4096  4096  2048  2048  4096  4096

...

For more rows see the link.

For the rational triangle R(n,m) see the example section of A244420.

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.

CROSSREFS

Cf. A084930, A244420, A000108.

Sequence in context: A022087 A095294 A190100 * A030168 A261212 A112435

Adjacent sequences:  A244418 A244419 A244420 * A244422 A244423 A244424

KEYWORD

nonn,easy,frac,tabl

AUTHOR

Wolfdieter Lang, Aug 04 2014

STATUS

approved

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Last modified October 20 15:22 EDT 2018. Contains 316388 sequences. (Running on oeis4.)