A028217 - OEIS

%I #20 Sep 08 2022 08:44:50

%S 1,37,865,16345,272881,4203577,61233985,856507465,11620866961,

%T 154020283417,2004281620705,25705179230185,325843083624241,

%U 4091525808208057,50980871394705025,631212806724858505,7774530598929024721,95344134061235633497,1165077358261678630945

%N Expansion of 1/((1-6x)(1-9x)(1-10x)(1-12x)).

%H Harvey P. Dale, <a href="/A028217/b028217.txt">Table of n, a(n) for n = 0..925</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (37,-504,2988,-6480).

%F a(n) = 22*a(n-1) - 120*a(n-2) + 3^n*(3^(n+1) - 2^(n+1)), with a(0)=1, a(1)=37. - _Vincenzo Librandi_, Mar 14 2011

%F a(n) = 37*a(n-1) - 504*a(n-2) + 2988*a(n-3) - 6480*a(n-4), a(0)=1, a(1)=37, a(2)=865, a(3)=16345. - _Vincenzo Librandi_, Mar 14 2011

%F a(n) = (2*12^(n+3)-9*10^(n+3)+8*9^(n+3)-6^(n+3))/72. [_Yahia Kahloune_, Jun 12 2013]

%p A028217:=n->(2*12^(n+3)-9*10^(n+3)+8*9^(n+3)-6^(n+3))/72; seq(A028217(n), n=0..20); # _Wesley Ivan Hurt_, Jun 28 2014

%t CoefficientList[Series[1/((1 - 6 x) (1 - 9 x) (1 - 10 x) (1 - 12 x)), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Jun 28 2014 *)

%t LinearRecurrence[{37,-504,2988,-6480},{1,37,865,16345},20] (* _Harvey P. Dale_, May 03 2022 *)

%o (Magma) [(2*12^(n+3)-9*10^(n+3)+8*9^(n+3)-6^(n+3))/72: n in [0..20] ]; // _Wesley Ivan Hurt_, Jun 28 2014

%o (PARI) Vec(1/((1-6*x)*(1-9*x)*(1-10*x)*(1-12*x))+ O(x^20)) \\ _Michel Marcus_, Jun 28 2014

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.