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Expansion of 1/((1-3x)(1-5x)(1-6x)(1-9x)).
0

%I #11 Jul 01 2015 16:50:47

%S 1,23,340,4130,45031,459893,4504690,42928160,401635861,3711270563,

%T 34005047440,309788905790,2811170579491,25442007146033,

%U 229842147512590,2073840099225020,18696506927851921,168462145714550303

%N Expansion of 1/((1-3x)(1-5x)(1-6x)(1-9x)).

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (23,-189,657,-810).

%F a(n)=(9^(n+3)-8*6^(n+3)+9*5^(n+3)-2*3^(n+3))/72. [_Yahia Kahloune_, Jun 07 2013]

%F a(0)=1, a(1)=23, a(2)=340, a(3)=4130, a(n)=23*a(n-1)-189*a(n-2)+ 657*a(n-3)- 810*a(n-4). - _Harvey P. Dale_, Jul 01 2015

%t CoefficientList[Series[1/((1-3x)(1-5x)(1-6x)(1-9x)),{x,0,30}],x] (* or *) LinearRecurrence[{23,-189,657,-810},{1,23,340,4130},30] (* _Harvey P. Dale_, Jul 01 2015 *)

%o (PARI) a(n)=(9^(n+3)-8*6^(n+3)+9*5^(n+3)-2*3^(n+3))/72 \\ _Charles R Greathouse IV_, Jun 07 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.