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A007701
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a(0) = 0; for n>0, a(n) = n^n*2^((n-1)^2).
(Formerly M4585)
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3
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0, 1, 8, 432, 131072, 204800000, 1565515579392, 56593444029595648, 9444732965739290427392, 7146646609494406531041460224, 24178516392292583494123520000000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Discriminant of Chebyshev polynomial T_n (x) of first kind.
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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).
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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].
Index entries for sequences related to Chebyshev polynomials.
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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(diff(T(n,x),x)|_{x=xn[i]},i=1..n), n>0, with the zeros xn[i],i=1..n, given above.
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PROG
| (PARI) a(n)=if(n<1, 0, n^n*2^((n-1)^2))
(PARI) a(n)=if(n<1, 0, poldisc(poltchebi(n)))
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CROSSREFS
| Cf. A086804.
Cf. A127670 (discriminant for S-polynomials).
Sequence in context: A024110 A132099 A186419 * A101356 A069442 A013457
Adjacent sequences: A007698 A007699 A007700 * A007702 A007703 A007704
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Additional comments from Michael Somos, Jun 26, 2002
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