%I #33 Jan 21 2025 14:24:41
%S 1,28,523,8218,117649,1592416,20790631,264958246,3320750557,
%T 41132364364,505211150899,6167574174034,74958865496425,
%U 908053837462072,10973667150086527,132377759927894782,1594780291608334453
%N Expansion of 1/((1-x)*(1-6*x)*(1-9*x)*(1-12*x)).
%H Vincenzo Librandi, <a href="/A024347/b024347.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (28,-261,882,-648).
%F a(n) = (20*12^(n+3) - 55*9^(n+3) + 44*6^(n+3) - 9)/3960. - _Yahia Kahloune_, Jun 28 2013
%F a(n) = 28*a(n-1) - 261*a(n-2) + 882*a(n-3) - 648*a(n-4) for n > 3; a(0)=1, a(1)=28, a(2)=523, a(3)=8218. - _Vincenzo Librandi_, Jul 16 2013
%F E.g.f.: (-9*exp(x) + 9504*exp(6*x) - 40095*exp(9*x) + 34560*exp(12*x))/3960. - _G. C. Greubel_, Jan 30 2022
%p A024347:= n -> (20*12^(n+3) - 55*9^(n+3) + 44*6^(n+3) -9)/3960; seq(A024347(n), n=0..20); # _G. C. Greubel_, Jan 30 2022
%t CoefficientList[Series[1/((1-x)(1-6x)(1-9x)(1-12x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 16 2013 *)
%o (PARI) Vec(1/((1-x)*(1-6*x)*(1-9*x)*(1-12*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-6*x)*(1-9*x)*(1-12*x)))); // _Vincenzo Librandi_, Jul 16 2013
%o (Magma) I:=[1, 28, 523, 8218]; [n le 4 select I[n] else 28*Self(n-1)-261*Self(n-2)+882*Self(n-3)-648*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 16 2013
%o (Sage) [(20*12^(n+3) - 55*9^(n+3) + 44*6^(n+3) -9)/3960 for n in (0..20)] # _G. C. Greubel_, Jan 30 2022
%Y Cf. A003464, A016244, A024346.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_