A024110 - OEIS

%I #17 Sep 08 2022 08:44:48

%S 1,8,-431,-18954,-255583,-1894076,-9546255,-35570638,-91171007,0,

%T 2486784401,29023111918,277269756129,2531261328956,22856131408177,

%U 205852688735274,1852951469375105,16677063111790072,150094436937708753

%N a(n) = 9^n - n^9.

%H Vincenzo Librandi, <a href="/A024110/b024110.txt">Table of n, a(n) for n = 0..300</a>

%F From _Chai Wah Wu_, Jan 26 2020: (Start)

%F a(n) = 19*a(n-1) - 135*a(n-2) + 525*a(n-3) - 1290*a(n-4) + 2142*a(n-5) - 2478*a(n-6) + 2010*a(n-7) - 1125*a(n-8) + 415*a(n-9) - 91*a(n-10) + 9*a(n-11) for n > 10.

%F G.f.: (-10*x^10 - 4507*x^9 - 131015*x^8 - 779378*x^7 - 1317686*x^6 - 637664*x^5 - 43448*x^4 + 10210*x^3 + 448*x^2 + 11*x - 1)/((x - 1)^10*(9*x - 1)). (End)

%t lst={}; Do[AppendTo[lst,9^n-n^9],{n,0,5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 15 2009 *)

%t Table[9^n-n^9,{n,0,20}] (* _Harvey P. Dale_, Jul 27 2022 *)

%o (Magma) [9^n-n^9: n in [0..20]]; // _Vincenzo Librandi_, Jun 30 2011

%Y Cf. A024012, A024026, A058794, A024040, A024054, A024068, A024082, A024096. - _Vladimir Joseph Stephan Orlovsky_, Jan 15 2009

%K sign,easy

%O 0,2

%A _N. J. A. Sloane_