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%I #12 Sep 08 2022 08:44:48
%S 1,3,-4080,-531377,-16776960,-244139601,-2176778240,-13841270817,
%T -68719411200,-282429274337,-999998951424,-3138424182417,
%U -8916083671040,-23298018013617,-56693643939840,-129745264148801,-281470681743360,-582605057360577,-1156762661949440
%N a(n) = 4^n - n^12.
%H Vincenzo Librandi, <a href="/A024048/b024048.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (17,-130,598,-1859,4147,-6864,8580,-8151,5863,-3146,1222,-325,53,-4).
%F From _Colin Barker_, Jan 30 2018: (Start)
%F G.f.: (1 - 14*x - 4001*x^2 - 462225*x^3 - 8273886*x^4 - 25569021*x^5 + 102763326*x^6 + 487535142*x^7 + 583731957*x^8 + 255085496*x^9 + 40272755*x^10 + 1908923*x^11 + 16344*x^12 + 3*x^13) / ((1 - x)^13*(1 - 4*x)).
%F a(n) = 17*a(n-1) - 130*a(n-2) + 598*a(n-3) - 1859*a(n-4) + 4147*a(n-5) - 6864*a(n-6) + 8580*a(n-7) - 8151*a(n-8) + 5863*a(n-9) - 3146*a(n-10) + 1222*a(n-11) - 325*a(n-12) + 53*a(n-13) - 4*a(n-14) for n>13.
%F (End)
%o (Magma) [4^n-n^12: n in [0..30]]; // _Vincenzo Librandi_, Jul 02 2011
%o (PARI) Vec((1 - 14*x - 4001*x^2 - 462225*x^3 - 8273886*x^4 - 25569021*x^5 + 102763326*x^6 + 487535142*x^7 + 583731957*x^8 + 255085496*x^9 + 40272755*x^10 + 1908923*x^11 + 16344*x^12 + 3*x^13) / ((1 - x)^13*(1 - 4*x)) + O(x^30)) \\ _Colin Barker_, Jan 30 2018
%K sign,easy
%O 0,2
%A _N. J. A. Sloane_
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