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 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 a(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(a(n,m)*(2*x)^(2*(n-m)+1), m=0..n). See the W. Lang link given in A053125. Unsigned version is mirror image of A078812 . [From 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 a(n, m) := 0 if n

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Last modified May 20 18:46 EDT 2018. Contains 304347 sequences. (Running on oeis4.)