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Expansion of 1/((1-8*x)*(1-10*x)*(1-11*x)*(1-12*x)).
11

%I #32 Sep 08 2022 08:44:40

%S 1,41,1055,21805,395871,6595701,103397575,1549123085,22414242191,

%T 315506452261,4343673465495,58723278269565,781995624847711,

%U 10282227616659221,133750220517219815,1723860289008683245

%N Expansion of 1/((1-8*x)*(1-10*x)*(1-11*x)*(1-12*x)).

%H Vincenzo Librandi, <a href="/A016093/b016093.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 (41,-626,4216,-10560).

%F G.f.: 1/((1-8*x)*(1-10*x)*(1-11*x)*(1-12*x)).

%F a(n) = -8^(2+n)/3 - 11^(n+3)/3 +25*10^(n+1) +18*12^(n+1). - _R. J. Mathar_, Mar 14 2011

%F a(n) = 41*a(n-1) -626*a(n-2) +4216*a(n-3) -10560*a(n-4), n>=4. - _Vincenzo Librandi_, Mar 18 2011

%F a(n) = 23*a(n-1) -132*a(n-2) +5*10^n-4*8^n, n>=2. - _Vincenzo Librandi_, Mar 18 2011

%t CoefficientList[Series[1 / ((1 - 8 x) (1 - 10 x) (1 - 11 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jun 24 2013 *)

%o (PARI) Vec(1/((1-8*x)*(1-10*x)*(1-11*x)*(1-12*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 23 2012

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-8*x)*(1-10*x)*(1-11*x)*(1-12*x)))); /* or */ I:=[1, 41, 1055, 21805]; [n le 4 select I[n] else 41*Self(n-1)-626*Self(n-2)+4216*Self(n-3)-10560*Self(n-4): n in [1..20]]; // _Vincenzo Librandi_, Jun 24 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_