A024022 - OEIS

%I #16 Dec 11 2022 15:07:34

%S 1,1,-4092,-531433,-16777200,-244140593,-2176782272,-13841287073,

%T -68719476480,-282429535969,-999999998976,-3138428374673,

%U -8916100444160,-23298085114289,-56693912358912,-129746337857857,-281474976645120

%N a(n) = 2^n - n^12.

%H Vincenzo Librandi, <a href="/A024022/b024022.txt">Table of n, a(n) for n = 0..230</a>

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (15, -104, 442, -1287, 2717, -4290, 5148, -4719, 3289, -1716, 650, -169, 27, -2).

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

%F a(n) = 15*a(n-1) - 104*a(n-2) + 442*a(n-3) - 1287*a(n-4) + 2717*a(n-5) - 4290*a(n-6) + 5148*a(n-7) - 4719*a(n-8) + 3289*a(n-9) - 1716*a(n-10) + 650*a(n-11) - 169*a(n-12) + 27*a(n-13) - 2*a(n-14) for n > 13.

%F G.f.: (x^13 + 8178*x^12 + 952381*x^11 + 19897385*x^10 + 122448548*x^9 + 258707385*x^8 + 162510570*x^7 - 29873622*x^6 - 45944391*x^5 - 9230428*x^4 - 470391*x^3 - 4003*x^2 - 14*x + 1)/((x - 1)^13*(2*x - 1)). (End)

%t CoefficientList[Series[(x^13+8178x^12+952381x^11+19897385x^10+122448548x^9+258707385x^8+162510570x^7-29873622x^6-45944391x^5-9230428x^4-470391x^3-4003x^2-14x+1)/((x-1)^13(2x-1)),{x,0,30}],x] (* or *) LinearRecurrence[{15,-104,442,-1287,2717,-4290,5148,-4719,3289,-1716,650,-169,27,-2},{1,1,-4092,-531433,-16777200,-244140593,-2176782272,-13841287073,-68719476480,-282429535969,-999999998976,-3138428374673,-8916100444160,-23298085114289},30] (* _Harvey P. Dale_, Dec 11 2022 *)

%o (Magma) [2^n-n^12: n in [0..30] ]; // _Vincenzo Librandi_, Apr 30 2011

%K sign

%O 0,3

%A _N. J. A. Sloane_