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A008312 Triangle of coefficients of Chebyshev polynomials U_n(x). 8

%I

%S 1,2,-1,4,-4,8,1,-12,16,6,-32,32,-1,24,-80,64,-8,80,-192,128,1,-40,

%T 240,-448,256,10,-160,672,-1024,512,-1,60,-560,1792,-2304,1024,-12,

%U 280,-1792,4608,-5120,2048

%N Triangle of coefficients of Chebyshev polynomials U_n(x).

%C Version with zeros in A053117. - _Philippe Deléham_, Nov 27 2013

%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 796.

%H T. D. Noe, <a href="/A008312/b008312.txt">Rows n=0..100 of triangle, flattened</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H D. Foata and G.-N. Han, <a href="http://www-irma.u-strasbg.fr/~foata/paper/pub71.html">Nombres de Fibonacci et polynomes orthogonaux</a>.

%H M. Janjic and B. Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv preprint arXiv:1301.4550, 2013. - From _N. J. A. Sloane_, Feb 13 2013

%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>

%e Triangle begins:

%e 1

%e 2

%e -1, 4

%e -4, 8

%e 1, -12, 16

%e 6, -32, 32

%e -1, 24, -80, 64

%e -8, 80, -192, 128

%e 1, -40, 240, -448, 256

%e 10, -160, 672, -1024, 512

%e -1, 60, -560, 1792, -2304, 1024

%e -12, 280, -1792, 4608, -5120, 2048...

%e With zeros, triangle begins:

%e 1

%e 0, 2

%e -1, 0, 4

%e 0, -4, 0, 8

%e 1, 0, -12, 0, 16

%e 0, 6, 0, -32, 0, 32

%e -1, 0, 24, 0, -80, 0, 64

%e 0, -8, 0, 80, 0, -192, 0, 128

%e 1, 0, -40, 0, 240, 0, -448, 0, 256

%e 0, 10, 0, -160, 0, 672, 0, -1024, 0, 512

%e -1, 0, 60, 0, -560, 0, 1792, 0, -2304, 0, 1024

%e 0, -12, 0, 280, 0, -1792, 0, 4608, 0, -5120, 0, 2048. - _Philippe Deléham_, Nov 27 2013

%t a[n_, k_] := Coefficient[ ChebyshevU[n, x], x, k]; row[n_] := Table[a[n, k], {k, Mod[n, 2], n, 2}]; Table[row[n], {n, 0, 11}] // Flatten (* _Jean-François Alcover_, Oct 03 2012 *)

%Y Reflected version with zeros: A053118. Cf. A008310, A053112, A053117.

%K sign,tabf,easy,nice

%O 0,2

%A _N. J. A. Sloane_.

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Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)