A272162 a(n) = n^5-n+1.

1, 1, 31, 241, 1021, 3121, 7771, 16801, 32761, 59041, 99991, 161041, 248821, 371281, 537811, 759361, 1048561, 1419841, 1889551, 2476081, 3199981, 4084081, 5153611, 6436321, 7962601, 9765601, 11881351, 14348881, 17210341, 20511121, 24299971, 28629121, 33554401, 39135361, 45435391

Offset: 0

Author

Benjamin Przybocki, Apr 23 2016

Keywords

• nonn
• easy

Comments

This is the simplest polynomial whose roots cannot be expressed in terms of radicals.

Links

• Wikipedia, Finding roots of a quintic equation
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A271209

Programs

Mathematica

Table[n^5 - n + 1, {n, 0, 34}] (* Michael De Vlieger, Apr 26 2016 *)

Formula

G.f.: ( 1-5*x+40*x^2+50*x^3+35*x^4-x^5 ) / (x-1)^6. - R. J. Mathar, Apr 26 2016