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

%I #21 Sep 08 2022 08:44:45

%S 1,15,148,1218,9079,63693,429346,2815296,18097717,114645531,718257904,

%T 4461736734,27532164115,169004094729,1033087293022,6293858904732,

%U 38239893731473,231823257614487,1402859602945900

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

%H Vincenzo Librandi, <a href="/A021414/b021414.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (15,-77,153,-90).

%F a(0)=1, a(1)=15, a(2)=148, a(3)=1218, a(n)=15*a(n-1)-77*a(n-2)+153*a(n-3)- 90*a(n-4). - _Harvey P. Dale_, Mar 31 2013

%F a(n) = (8*6^(n+3)-15*5^(n+3)+10*3^(n+3)-3)/120. - _Yahia Kahloune_, May 07 2013

%F a(0)=1, a(1)=15; for n>1, a(n) = 11*a(n-1) -30*a(n-2) +(3^n-1)/2. - _Vincenzo Librandi_, Jul 09 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 5 x) (1 - 6 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{15, -77, 153, -90}, {1, 15, 148, 1218}, 30] (* _Harvey P. Dale_, Mar 31 2013 *)

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-5*x)*(1-6*x)))); /* or */ I:=[1, 15, 148, 1218]; [n le 4 select I[n] else 15*Self(n-1)-77*Self(n-2)+153*Self(n-3)-90*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 09 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.