%I #14 Apr 12 2023 08:15:28
%S 1,22,335,4460,56061,686802,8317435,100210120,1204613321,14466168782,
%T 173649468135,2084076423780,25010353485781,300131513309962,
%U 3601614875036435,43219563508677440,518635692871953441
%N Expansion of 1/((1-x)(1-4x)(1-5x)(1-12x)).
%H Vincenzo Librandi, <a href="/A021794/b021794.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 (22,-149,368,-240).
%F G.f.: 1/((1-x)*(1-4*x)*(1-5*x)*(1-12*x)).
%F a(n) = -1/132 +2^(2n+3)/3 -5^(n+3)/28 +2^(2n+3)*3^(n+3)/77. - _Bruno Berselli_, May 08 2013
%F a(n) = 22*a(n-1) - 149*a(n-2) + 368*a(n-3) - 240*a(n-4). - _Wesley Ivan Hurt_, Apr 12 2023
%t CoefficientList[Series[1/((1-x) (1-4 x) (1-5 x) (1-12 x)), {x, 0, 20}], x] (* _Bruno Berselli_, May 08 2013 *)
%o (PARI) Vec(1/((1-x)*(1-4*x)*(1-5*x)*(1-12*x))+O(x^20)) \\ _Bruno Berselli_, May 08 2013
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-4*x)*(1-5*x)*(1-12*x)))); // _Bruno Berselli_, May 08 2013
%Y Cf. A019041 (first differences).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.