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%I #18 Sep 08 2022 08:44:46
%S 1,26,455,6760,92301,1200966,15177955,188364020,2310685001,
%T 28133195506,340850357055,4116281407680,49604299052101,
%U 596924491783646,7176484756065755,86224982057057740,1035557295293705601
%N Expansion of 1/((1-x)*(1-5*x)*(1-8*x)*(1-12*x)).
%H Vincenzo Librandi, <a href="/A022725/b022725.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 (26,-221,676,-480).
%F a(n) = (3*12^(n+3) - 11*8^(n+3) + 11*5^(n+3) - 3)/924. - _Yahia Kahloune_, Jun 29 2013
%F a(0)=1, a(1)=26, a(2)=455, a(3)=6760; for n>3, a(n) = 26*a(n-1) -221*a(n-2) +676*a(n-3) -480*a(n-4). - _Vincenzo Librandi_, Jul 12 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 8 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 12 2013 *)
%o (Magma) I:=[1,26,455,6760]; [n le 4 select I[n] else 26*Self(n-1)-221*Self(n-2)+676*Self(n-3)-480*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-8*x)*(1-12*x)))); // _Vincenzo Librandi_, Jul 12 2013
%o (PARI) x='x+O('x^30); Vec(1/((1-x)*(1-5*x)*(1-8*x)*(1-12*x))) \\ _G. C. Greubel_, Jul 25 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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