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Expansion of 1/((1-x)*(1-2x)*(1-6x)*(1-12x)).
1

%I #25 Sep 08 2022 08:44:45

%S 1,21,313,4137,51961,637497,7733881,93310329,1122747001,13491103353,

%T 162002078329,1944677972601,23340053875321,280104155744889,

%U 3361390924417657,40337537425951353,484055527109184121

%N Expansion of 1/((1-x)*(1-2x)*(1-6x)*(1-12x)).

%H Vincenzo Librandi, <a href="/A021214/b021214.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 (21,-128,252,-144).

%F a(n) = (2*12^(n+3) - 11*6^(n+3) + 33*2^(n+3) - 24)/1320. - _Yahia Kahloune_, May 19 2013

%F a(0)=1, a(1)=21, a(2)=313, a(3)=4137; for n>3, a(n) = 21*a(n-1) -128*a(n-2) +252*a(n-3)-144*a(n-4). - _Vincenzo Librandi_, Jul 08 2013

%F a(0)=1, a(1)=21; for n>1, a(n) = 18*a(n-1) -72*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 08 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 6 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 08 2013 *)

%t LinearRecurrence[{21,-128,252,-144},{1,21,313,4137},30] (* _Harvey P. Dale_, Mar 07 2015 *)

%o (Magma) I:=[1, 21, 313, 4137]; [n le 4 select I[n] else 21*Self(n-1)-128*Self(n-2)+252*Self(n-3)-144*Self(n-4): n in [1..25]]; /* or */ I:=[1, 21]; [n le 2 select I[n] else 18*Self(n-1)-72*Self(n-2)+2^n-1: n in [1..20]]; // _Vincenzo Librandi_, Jul 08 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.