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 A007701 a(0) = 0; for n > 0, a(n) = n^n*2^((n-1)^2). (Formerly M4585) 8
 0, 1, 8, 432, 131072, 204800000, 1565515579392, 56593444029595648, 9444732965739290427392, 7146646609494406531041460224, 24178516392292583494123520000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Discriminant of Chebyshev polynomial T_n (x) of first kind. 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; p. 219. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). 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]. FORMULA a(n) = (n^n)*2^((n-1)^2), n >= 1, a(0):=0. a(n) = ((2^((n-1)^2))*Det(Vn(xn[1],...,xn[n])))^2, n >= 1, with the determinant of the Vandermonde matrix Vn with elements (Vn)i,j:= xn[i]^j, i=1..n,j=0..n-1 and xn[i]:=cos((2*i-1)*Pi/(2*n)), i=1..n, are the zeros of the Chebyshev T(n,x) polynomials. a(n) = ((-1)^(n*(n-1)/2))*(2^((n-1)*(n-2))) * Product_{i=1..n} ((d/dx)T(n,x)|_{x=xn[i]}), n > 0, with the zeros xn[i], i=1..n, given above. PROG (PARI) a(n)=if(n<1, 0, n^n*2^((n-1)^2)) (PARI) a(n)=if(n<1, 0, poldisc(poltchebi(n))) CROSSREFS Cf. A086804. Cf. A127670 (discriminant for S-polynomials). Sequence in context: A024110 A132099 A186419 * A101356 A231102 A231824 Adjacent sequences:  A007698 A007699 A007700 * A007702 A007703 A007704 KEYWORD nonn AUTHOR EXTENSIONS Additional comments from Michael Somos, Jun 26 2002 STATUS approved

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Last modified May 26 14:46 EDT 2020. Contains 334626 sequences. (Running on oeis4.)