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Search: id:A127670
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| 1, 4, 32, 400, 6912, 153664, 4194304, 136048896, 5120000000, 219503494144, 10567230160896, 564668382613504, 33174037869887488, 2125764000000000000, 147573952589676412928, 11034809241396899282944, 884295678882933431599104
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OFFSET
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1,2
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REFERENCES
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Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990; p. 219 for T and U polynomials.
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FORMULA
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a(n)= ((n+1)^{n-2})*2^n, n>=1.
a(n)= Det(Vn(xn[1],..,xn[n]))^2 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]:=2*cos(Pi*i/(n+1)), i=1,..,n, are the zeros of S(n,x):=U(n,x/2).
a(n)= ((-1)^(n*(n-1)/2))*product(diff(S(n,x))|_{x=xn[j]},j=1..n)), n>=1, with the zeros xn[j],j=1..n, given above.
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CROSSREFS
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Cf. A007701 (T-polynomials), A086804 (U-polynomials).
Sequence in context: A007763 A005263 A113131 this_sequence A005172 A140178 A088991
Adjacent sequences: A127667 A127668 A127669 this_sequence A127671 A127672 A127673
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jan 23 2007
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