cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A086783 Discriminant of the polynomial x^n - 1.

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%I A086783 #31 Mar 18 2021 08:29:57
%S A086783 1,4,-27,-256,3125,46656,-823543,-16777216,387420489,10000000000,
%T A086783 -285311670611,-8916100448256,302875106592253,11112006825558016,
%U A086783 -437893890380859375,-18446744073709551616,827240261886336764177,39346408075296537575424,-1978419655660313589123979
%N A086783 Discriminant of the polynomial x^n - 1.
%C A086783 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 A086783 Kenneth G. Hawes, <a href="/A086783/b086783.txt">Table of n, a(n) for n = 1..386</a>
%H A086783 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 A086783 a(n) = (-1)^floor((n-1)/2) * n^n = (-1)^floor((n-1)/2) * A000312(n).
%o A086783 (Sage) def A086783(n) : return (-1)^((n-1)//2) * n^n # _Eric M. Schmidt_, May 04 2013
%o A086783 (PARI) a(n)=poldisc('x^n-1); \\ _Joerg Arndt_, May 04 2013
%Y A086783 Cf. A000312, A004124.
%K A086783 sign,easy
%O A086783 1,2
%A A086783 Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 03 2003
%E A086783 More terms from _Eric M. Schmidt_, May 04 2013