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%I #13 Sep 08 2022 08:44:45
%S 1,25,437,6629,93429,1260021,16509109,211998133,2682866357,
%T 33583284917,416888307381,5141548576437,63087471804085,
%U 770938550533813,9390151495286453,114070706832309941,1382737370876575413
%N Expansion of 1/((1-x)(1-2x)(1-10x)(1-12x)).
%H Vincenzo Librandi, <a href="/A021324/b021324.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 (25,-188,404,-240).
%F a(n) = (36*12^(n+3) - 55*10^(n+3) + 99*2^(n+3) - 80)/7920. [_Yahia Kahloune_, Jul 07 2013]
%F a(0)=1, a(1)=25; for n>1, a(n) = 22*a(n-1) -120*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 09 2013
%F a(0)=1, a(1)=25, a(2)=437, a(3)=6629; for n>3, a(n) = 25*a(n-1) -188*a(n-2) +404*a(n-3) -240*a(n-4). - _Vincenzo Librandi_, Jul 09 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 10 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 09 2013 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-10*x)*(1-12*x)))); /* or */ I:=[1, 25, 437, 6629]; [n le 4 select I[n] else 25*Self(n-1)-188*Self(n-2)+404*Self(n-3)-240*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 09 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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