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%I #22 Jan 31 2022 03:16:51
%S 1,15,163,1563,14059,121803,1030411,8579211,70649227,577287051,
%T 4690855819,37962203019,306309762955,2466150936459,19823244488587,
%U 159150177890187,1276586755010443,10233006031417227,81985920199339915
%N Expansion of 1/((1-x)*(1-6*x)*(1-8*x)).
%H G. C. Greubel, <a href="/A016243/b016243.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15,-62,48).
%F a(n) = 14*a(n-1) - 48*a(n-2) + 1 with a(0)=1, a(1)=15. - _Vincenzo Librandi_, Feb 10 2011
%F a(n) = (5*8^(n+2) - 7*6^(n+2) + 2)/70. - _Yahia Kahloune_, May 19 2013
%F E.g.f.: (1/35)*(exp(x) - 126*exp(6*x) + 160*exp(8*x)). - _G. C. Greubel_, Jan 30 2022
%t Table[(5*8^(n + 2) - 7*6^(n + 2) + 2)/70, {n, 0, 20}] (* _Wesley Ivan Hurt_, Jun 06 2014 *)
%o (Magma) [(5*8^(n+2) - 7*6^(n+2) + 2)/70 : n in [0..50]]; // _Wesley Ivan Hurt_, Jun 06 2014
%o (Sage) [(20*8^(n+1) -21*6^(n+1) +1)/35 for n in (0..30)] # _G. C. Greubel_, Jan 30 2022
%Y Cf. A003464, A016244.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 11 1999
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