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%I #15 Sep 08 2022 08:44:48
%S 1,23,348,4378,49679,528381,5380306,53132816,513181317,4875626899,
%T 45752166824,425305531014,3925114125115,36023250380777,
%U 329183853207102,2998041099306172,27233460168740273,246879085434889215
%N Expansion of 1/((1-x)(1-6x)(1-7x)(1-9x)).
%H Vincenzo Librandi, <a href="/A023950/b023950.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 (23,-181,537,-378).
%F a(n) = (5*9^(n+3)-20*7^(n+3)+16*6^(n+3)-1)/240. [_Yahia Kahloune_, May 25 2013]
%F a(0)=1, a(1)=23, a(2)=348, a(3)=4378; for n>3, a(n) = 23*a(n-1) -181*a(n-2) +537*a(n-3) -378*a(n-4). - _Vincenzo Librandi_, Jul 12 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 6 x) (1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 12 2013 *)
%o (Magma) I:=[1, 23, 348, 4378]; [n le 4 select I[n] else 23*Self(n-1)-181*Self(n-2)+537*Self(n-3)-378*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-6*x)*(1-7*x)*(1-9*x)))); // _Vincenzo Librandi_, Jul 12 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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