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%I #16 Aug 28 2020 06:17:06
%S 1,-3,-31,229,3381,-43531,-870199,15953673,404197705,-9612579511,
%T -295311670611,8630788777645,311791207040509,-10809131718965763,
%U -449005897206417391,18008850183328692241,845687005960046315793,-38519167813410200811247
%N Discriminant of the polynomial x^n + x + 1.
%C Except for the sign, the sequence alternates between the sum and difference of consecutive terms of A000312. x^2+x+1 divides x^n+x+1 for n=2 (mod 3).
%D Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012.
%F for n>1, a(n) = (n^n + (-1)^(n-1) * (n-1)^(n-1)) * (-1)^floor(n/2).
%F a(n) = (Cos[Pi n/2]+Sin[Pi n/2])(n^n)+(Cos[Pi(n+1)/2]+Sin[Pi(n+1)/2])(n+1)^(n+1). - _Artur Jasinski_, Oct 12 2007
%t Table[Discriminant[x^n + x + 1, x], {n, 0, 100}] (* _Artur Jasinski_, Oct 12 2007 *)
%o (PARI) a(n) = poldisc(x^n+x+1); \\ _Michel Marcus_, Aug 28 2020
%Y Cf. A000312 (n^n), A007781 (n^n - (n-1)^(n-1)), A056788 (n^n + (n-1)^(n-1)), A086797 (discriminant of the polynomial x^n-x-1).
%K sign
%O 1,2
%A _T. D. Noe_, Dec 21 2005