The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A053123 Triangle of coefficients of shifted Chebyshev's S(n,x-2)= U(n,x/2-1) polynomials (exponents of x in decreasing order). 14
 1, 1, -2, 1, -4, 3, 1, -6, 10, -4, 1, -8, 21, -20, 5, 1, -10, 36, -56, 35, -6, 1, -12, 55, -120, 126, -56, 7, 1, -14, 78, -220, 330, -252, 84, -8, 1, -16, 105, -364, 715, -792, 462, -120, 9, 1, -18, 136, -560, 1365, -2002, 1716, -792, 165, -10, 1, -20, 171, -816, 2380, -4368, 5005, -3432, 1287, -220, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS T(n,m)= A053122(n,n-m). G.f. for row polynomials and row sums same as in A053122. Unsigned column sequences are A000012, A005843, A014105, A002492 for m=0..3, resp. and A053126-A053131 for m=4..9. This is also the coefficient triangle for Chebyshev's U(2*n+1,x) polynomials expanded in decreasing odd powers of (2*x): U(2*n+1,x) = Sum_{m=0..n} (T(n,m)*(2*x)^(2*(n-m)+1). See the W. Lang link given in A053125. Unsigned version is mirror image of A078812. - Philippe Deléham, Dec 02 2008 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. 795 Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990. Stephen Barnett, "Matrices: Methods and Applications", Oxford University Press, 1990, p. 132, 343. LINKS T. D. Noe, Rows n=0..50 of triangle, flattened 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]. FORMULA T(n, m) = 0 if n List([0..n], k-> (-1)^k*Binomial(2*n-k+1, k) ))); # G. C. Greubel, Jul 23 2019 CROSSREFS Cf. A053124, A053122, A172431. Sequence in context: A132191 A094437 A172431 * A107661 A126570 A048790 Adjacent sequences:  A053120 A053121 A053122 * A053124 A053125 A053126 KEYWORD easy,sign,tabl AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 2 16:47 EDT 2020. Contains 335404 sequences. (Running on oeis4.)