A086797 - OEIS

%I #22 Jun 23 2019 02:24:32

%S 0,5,-23,-283,2869,49781,-776887,-17600759,370643273,10387420489,

%T -275311670611,-9201412118867,293959006143997,11414881932150269,

%U -426781883555301359,-18884637964090410991,808793517812627212561,40173648337182874339601

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

%C Selmer proved that for all n the Galois group of the polynomial x^n - x - 1 over the rationals is the symmetric group S_n. [Comment corrected by _Artur Jasinski_, Feb 06 2007]

%H Mohammad K. Azarian, <a href="http://www.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. 251-257.  Mathematical Reviews, MR2312537.  Zentralblatt MATH, Zbl 1133.11012.

%H H. Osada, <a href="https://doi.org/10.1016/0022-314X(87)90029-1">The Galois groups of the polynomials X^n + a X^l + b</a>, Journal of Number Theory, Feb. 1987, vol. 25, (no.2):230-8.

%H Ernst S. Selmer, <a href="https://doi.org/10.7146/math.scand.a-10478">On the irreducibility of certain trinomials</a>, Math. Scand., 4 (1956) 287-302.

%F Except for the sign, the sequence alternates between the sum and difference of consecutive terms of A000312. a(n) = (n^n + (-1)^n (n-1)^(n-1))*(-1)^ceiling(1+n/2). - _T. D. Noe_, Aug 13 2004

%o (PARI) a(n)=poldisc(x^n-x-1)

%Y Cf. A000312 (n^n), A007781 (n^n - (n-1)^(n-1)), A056788 (n^n + (n-1)^(n-1)).

%Y Cf. A086783.

%K sign

%O 1,2

%A Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 05 2003

%E More terms from _Benoit Cloitre_, Aug 06 2003