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%I #20 Sep 08 2022 08:44:45
%S 1,21,295,3465,36751,365001,3463615,31794105,284628751,2499039081,
%T 21606842335,184519243545,1559982264751,13079717026761,
%U 108915112739455,901732722577785,7429565635164751,60963378722560041,498496565225842975,4064108629664292825,33049477950757248751
%N Expansion of 1/((1-6*x)*(1-7*x)*(1-8*x)).
%H Vincenzo Librandi, <a href="/A020570/b020570.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-146,336).
%F If we define f(m,j,x) = Sum_{k=j..m} (binomial(m,k)*stirling2(k,j)*x^(m-k)) then a(n-2)=f(n,2,6), (n>=2). - _Milan Janjic_, Apr 26 2009
%F a(n) = 18*6^n -49*7^n +32*8^n. - _R. J. Mathar_, Jun 30 2013
%F a(0)=1, a(1)=21, a(2)=295; for n>2, a(n) = 21*a(n-1) -146*a(n-2) +336*a(n-3). - _Vincenzo Librandi_, Jul 04 2013
%F a(n) = 15*a(n-1) -56*a(n-2) +6^n. - _Vincenzo Librandi_, Jul 04 2013
%t CoefficientList[Series[1/((1-6*x)*(1-7*x)*(1-8*x)), {x, 0, 20}], x] (* _Harvey P. Dale_, Feb 24 2011 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-7*x)*(1-8*x)))); /* or */ I:=[1, 21, 295]; [n le 3 select I[n] else 21*Self(n-1)-146*Self(n-2)+336*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 04 2013
%o (PARI) x='x+O('x^30); Vec(1/((1-6*x)*(1-7*x)*(1-8*x))) \\ _G. C. Greubel_, Feb 07 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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