A024054 a(n) = 5^n - n^5.

1, 4, -7, -118, -399, 0, 7849, 61318, 357857, 1894076, 9665625, 48667074, 243891793, 1220331832, 6102977801, 30516818750, 152586842049, 762938033268, 3814695376057, 19073483852026, 95367428440625

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (11, -45, 95, -115, 81, -31, 5).

Crossrefs

Cf. A024012, A024026, A058794, A024040. - Vladimir Joseph Stephan Orlovsky, Jan 15 2009

Programs

Magma

[5^n-n^5: n in [0..30]]; // Vincenzo Librandi, May 14 2011

Mathematica

lst={}; Do[AppendTo[lst,5^n-n^5],{n,0,5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 15 2009 *)
Table[5^n-n^5,{n,0,20}] (* or *) LinearRecurrence[{11,-45,95,-115,81,-31,5},{1,4,-7,-118,-399,0,7849},30] (* Harvey P. Dale, Oct 15 2014 *)

PARI

a(n)=5^n-n^5 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: (-6*x^6 - 123*x^5 - 319*x^4 - 44*x^3 + 6*x^2 + 7*x - 1)/((x - 1)^6*(5*x - 1)). - Harvey P. Dale, Oct 15 2014

a(0)=1, a(1)=4, a(2)=-7, a(3)=-118, a(4)=-399, a(5)=0, a(6)=7849, a(n) = 11*a(n-1) - 45*a(n-2) + 95*a(n-3) - 115*a(n-4) + 81*a(n-5) - 31*a(n-6) + 5*a(n-7). - Harvey P. Dale, Oct 15 2014