%I #22 May 04 2017 00:19:12
%S 1,14,148,1400,12496,107744,908608,7548800,62070016,506637824,
%T 4113568768,33271347200,268347559936,2159841173504,17357093552128,
%U 139326933401600,1117436577120256,8956419276406784,71752914167922688
%N Expansion of 1/((1-6x)(1-8x)).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-48)
%F a(n) = Sum_{k=1..n} 2^(n-1)*3^(n-k)*binomial(n,k). - _Zerinvary Lajos_, Sep 24 2006
%F a(n) = 4*8^n-3*6^n = A081201(n+1). Binomial transform of A081033. [_R. J. Mathar_, Sep 18 2008]
%F a(n) = 8*a(n-1)+6^n. [_Vincenzo Librandi_, Feb 09 2011]
%F a(0)=1, a(1)=14, a(n) = 14*a(n-1)-48*a(n-2) [_Harvey P. Dale_, Dec 08 2011]
%p A016170:=n->4*8^n-3*6^n: seq(A016170(n), n=0..30); # _Wesley Ivan Hurt_, May 03 2017
%t CoefficientList[Series[1/((1-6x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[{14,-48},{1,14},30] (* _Harvey P. Dale_, Dec 08 2011 *)
%o (PARI) Vec(1/((1-6*x)*(1-8*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 24 2012
%Y Cf. A081033, A081201.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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