A024070 - OEIS

%I #15 Sep 08 2022 08:44:48

%S 1,5,-220,-6345,-64240,-382849,-1632960,-5484865,-15097600,-32969025,

%T -39533824,148438175,1746800640,12244963295,76888375040,467622093951,

%U 2816814940160,16919683687295,101548936707840

%N a(n) = 6^n-n^8.

%H Vincenzo Librandi, <a href="/A024070/b024070.txt">Table of n, a(n) for n = 0..500</a>

%F From _Chai Wah Wu_, May 13 2017: (Start)

%F a(n) = 15*a(n-1) - 90*a(n-2) + 300*a(n-3) - 630*a(n-4) + 882*a(n-5) - 840*a(n-6) + 540*a(n-7) - 225*a(n-8) + 55*a(n-9) - 6*a(n-10) for n > 9.

%F G.f.: (5*x^9 + 1490*x^8 + 25475*x^7 + 89505*x^6 + 77969*x^5 + 10265*x^4 - 2895*x^3 - 205*x^2 - 10*x + 1)/((x - 1)^9*(6*x - 1)). (End)

%p A024070:=n->6^n-n^8: seq(A024070(n), n=0..30); # _Wesley Ivan Hurt_, Apr 26 2017

%t Array[6^# - #^8 &, 19, 0] (* or *)

%t CoefficientList[Series[(5 x^9 + 1490 x^8 + 25475 x^7 + 89505 x^6 + 77969 x^5 + 10265 x^4 - 2895 x^3 - 205 x^2 - 10 x + 1)/((x - 1)^9*(6 x - 1)), {x, 0, 18}], x] (* _Michael De Vlieger_, May 13 2017 *)

%o (Magma) [6^n-n^8: n in [0..25]]; // _Vincenzo Librandi_, Jul 03 2011

%K sign,easy

%O 0,2

%A _N. J. A. Sloane_