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%I #16 Sep 08 2022 08:44:44
%S 1,23,362,4870,60411,715533,8243572,93366380,1046230421,11644889443,
%T 129058033182,1426436938290,15738640474831,173461105001753,
%U 1910430676985192,21031277618176600,231459987587209641
%N Expansion of 1/((1-5x)(1-7x)(1-11x)).
%H Vincenzo Librandi, <a href="/A020000/b020000.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,-167,385)
%F a(n) = 5^(n+2)/12+11^(n+2)/24-7^(n+2)/8. - R. J. Mathar, Mar 15 2011
%F a(0)=1, a(1)=23, a(2)=362; for n>2, a(n) = 23*a(n-1) -167*a(n-2) +385*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F a(n) = 18*a(n-1) -77*a(n-2) +5^n. - _Vincenzo Librandi_, Jul 03 2013
%t CoefficientList[Series[1 / ((1 - 5 x) (1 - 7 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)
%o (PARI) Vec(1/((1-5*x)*(1-7*x)*(1-11*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-7*x)*(1-11*x)))); /* or */ I:=[1, 23, 362]; [n le 3 select I[n] else 23*Self(n-1)-167*Self(n-2)+385*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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