A086783 - OEIS

%I #31 Mar 18 2021 08:29:57

%S 1,4,-27,-256,3125,46656,-823543,-16777216,387420489,10000000000,

%T -285311670611,-8916100448256,302875106592253,11112006825558016,

%U -437893890380859375,-18446744073709551616,827240261886336764177,39346408075296537575424,-1978419655660313589123979

%N Discriminant of the polynomial x^n - 1.

%C By definition, a(n) = Product_{1<=i<j<=n} (r^i - r^j)^2, where r = exp(2*Pi*i/n). As a result we have a(n) = det(M)^2, where M is the n X n matrix M_{jk} = r^(s(j)*t(k)), defined for any permutations {s(1), s(2), ..., s(n)},  {t(1), t(2), ..., t(n)} of {1,2,...n}. - _Jianing Song_, Mar 17 2021

%H Kenneth G. Hawes, <a href="/A086783/b086783.txt">Table of n, a(n) for n = 1..386</a>

%H Mohammad K. Azarian, <a href="http://ijpam.eu/contents/2007-36-2/9/9.pdf">On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials</a>, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 249-255. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012.

%F a(n) = (-1)^floor((n-1)/2) * n^n = (-1)^floor((n-1)/2) * A000312(n).

%o (Sage) def A086783(n) : return (-1)^((n-1)//2) * n^n # _Eric M. Schmidt_, May 04 2013

%o (PARI) a(n)=poldisc('x^n-1); \\ _Joerg Arndt_, May 04 2013

%Y Cf. A000312, A004124.

%K sign,easy

%O 1,2

%A Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 03 2003

%E More terms from _Eric M. Schmidt_, May 04 2013