This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A008312 #32 Dec 17 2021 08:12:39 %S A008312 1,2,-1,4,-4,8,1,-12,16,6,-32,32,-1,24,-80,64,-8,80,-192,128,1,-40, %T A008312 240,-448,256,10,-160,672,-1024,512,-1,60,-560,1792,-2304,1024,-12, %U A008312 280,-1792,4608,-5120,2048 %N A008312 Triangle of coefficients of Chebyshev polynomials U_n(x). %C A008312 Version with zeros in A053117. - _Philippe Deléham_, Nov 27 2013 %D A008312 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 A008312 T. D. Noe, <a href="/A008312/b008312.txt">Rows n = 0..100 of triangle, flattened</a> %H A008312 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 A008312 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 A008312 Valentin Ovsienko, <a href="https://arxiv.org/abs/2103.10800">Towards quantized complex numbers: q-deformed Gaussian integers and the Picard group</a>, arXiv:2103.10800 [math.QA], 2021. %H A008312 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 A008312 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a> %e A008312 From _Philippe Deléham_, Nov 27 2013: (Start) %e A008312 Triangle begins: %e A008312 1; %e A008312 2; %e A008312 -1, 4; %e A008312 -4, 8; %e A008312 1, -12, 16; %e A008312 6, -32, 32; %e A008312 -1, 24, -80, 64; %e A008312 -8, 80, -192, 128; %e A008312 1, -40, 240, -448, 256; %e A008312 10, -160, 672, -1024, 512; %e A008312 -1, 60, -560, 1792, -2304, 1024; %e A008312 -12, 280, -1792, 4608, -5120, 2048; %e A008312 ... %e A008312 With zeros, triangle begins: %e A008312 1; %e A008312 0, 2; %e A008312 -1, 0, 4; %e A008312 0, -4, 0, 8; %e A008312 1, 0, -12, 0, 16; %e A008312 0, 6, 0, -32, 0, 32; %e A008312 -1, 0, 24, 0, -80, 0, 64; %e A008312 0, -8, 0, 80, 0, -192, 0, 128; %e A008312 1, 0, -40, 0, 240, 0, -448, 0, 256; %e A008312 0, 10, 0, -160, 0, 672, 0, -1024, 0, 512; %e A008312 -1, 0, 60, 0, -560, 0, 1792, 0, -2304, 0, 1024; %e A008312 0, -12, 0, 280, 0, -1792, 0, 4608, 0, -5120, 0, 2048; %e A008312 ... %e A008312 (End) %t A008312 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 A008312 Reflected version with zeros: A053118. Cf. A008310, A053112, A053117. %K A008312 sign,tabf,easy,nice %O A008312 0,2 %A A008312 _N. J. A. Sloane_