login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A008312
Triangle of coefficients of Chebyshev polynomials U_n(x).
8
1, 2, -1, 4, -4, 8, 1, -12, 16, 6, -32, 32, -1, 24, -80, 64, -8, 80, -192, 128, 1, -40, 240, -448, 256, 10, -160, 672, -1024, 512, -1, 60, -560, 1792, -2304, 1024, -12, 280, -1792, 4608, -5120, 2048
OFFSET
0,2
COMMENTS
Version with zeros in A053117. - Philippe Deléham, Nov 27 2013
REFERENCES
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.
LINKS
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550, 2013. - From N. J. A. Sloane, Feb 13 2013
EXAMPLE
From Philippe Deléham, Nov 27 2013: (Start)
Triangle begins:
1;
2;
-1, 4;
-4, 8;
1, -12, 16;
6, -32, 32;
-1, 24, -80, 64;
-8, 80, -192, 128;
1, -40, 240, -448, 256;
10, -160, 672, -1024, 512;
-1, 60, -560, 1792, -2304, 1024;
-12, 280, -1792, 4608, -5120, 2048;
...
With zeros, triangle begins:
1;
0, 2;
-1, 0, 4;
0, -4, 0, 8;
1, 0, -12, 0, 16;
0, 6, 0, -32, 0, 32;
-1, 0, 24, 0, -80, 0, 64;
0, -8, 0, 80, 0, -192, 0, 128;
1, 0, -40, 0, 240, 0, -448, 0, 256;
0, 10, 0, -160, 0, 672, 0, -1024, 0, 512;
-1, 0, 60, 0, -560, 0, 1792, 0, -2304, 0, 1024;
0, -12, 0, 280, 0, -1792, 0, 4608, 0, -5120, 0, 2048;
...
(End)
MATHEMATICA
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 *)
CROSSREFS
Reflected version with zeros: A053118. Cf. A008310, A053112, A053117.
Sequence in context: A077965 A077967 A296188 * A345442 A060723 A300622
KEYWORD
sign,tabf,easy,nice
STATUS
approved