# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a007701 Showing 1-1 of 1 %I A007701 M4585 #26 Sep 04 2023 12:53:29 %S A007701 0,1,8,432,131072,204800000,1565515579392,56593444029595648, %T A007701 9444732965739290427392,7146646609494406531041460224, %U A007701 24178516392292583494123520000000000 %N A007701 a(0) = 0; for n > 0, a(n) = n^n*2^((n-1)^2). %C A007701 Discriminant of Chebyshev polynomial T_n (x) of first kind. %D A007701 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. %D A007701 Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990; p. 219. %D A007701 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A007701 Delbert L. Johnson, Table of n, a(n) for n = 0..55 %H A007701 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]. %H A007701 Index entries for sequences related to Chebyshev polynomials. %F A007701 a(n) = (n^n)*2^((n-1)^2), n >= 1, a(0):=0. %F A007701 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. %F A007701 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. %t A007701 Join[{0},Table[n^n 2^(n-1)^2,{n,10}]] (* _Harvey P. Dale_, Sep 04 2023 *) %o A007701 (PARI) a(n)=if(n<1,0,n^n*2^((n-1)^2)) %o A007701 (PARI) a(n)=if(n<1,0,poldisc(poltchebi(n))) %Y A007701 Cf. A086804. %Y A007701 Cf. A127670 (discriminant for S-polynomials). %K A007701 nonn %O A007701 0,3 %A A007701 _N. J. A. Sloane_ %E A007701 Additional comments from _Michael Somos_, Jun 26 2002 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE