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%I #18 Jan 31 2022 03:18:23
%S 1,16,187,1942,19033,180628,1681639,15470674,141251605,1283357680,
%T 11622778531,105040363246,947975408017,8547451504972,77021100541663,
%U 693754126856458,6247172473597069,56244864253707304
%N Expansion of 1/((1-x)*(1-6*x)*(1-9*x)).
%H G. C. Greubel, <a href="/A016244/b016244.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 (16,-69,54).
%F a(n) = (1 - 96*6^n + 135*9^n)/40. - Neven Juric, Oct 22 2009
%F a(0)=1, a(1)=16, a(n) = 15*a(n-1) - 54*a(n-2) + 1. - _Vincenzo Librandi_, Feb 10 2011
%F E.g.f.: (1/40)*(exp(x) - 96*exp(6*x) + 135*exp(9*x)). - _G. C. Greubel_, Jan 30 2022
%t LinearRecurrence[{16,-69,54}, {1,16,187}, 41] (* _G. C. Greubel_, Jan 30 2022 *)
%o (PARI) Vec(1/((1-x)*(1-6*x)*(1-9*x)) + O(x^40)) \\ _Michel Marcus_, Sep 04 2017
%o (Magma) [(1 -96*6^n +135*9^n)/40: n in [0..40]]; // _G. C. Greubel_, Jan 30 2022
%o (Sage) [(1 -16*6^(n+1) +15*9^(n+1))/40 for n in (0..40)] # _G. C. Greubel_, Jan 30 2022
%Y Cf. A003464, A024346, A024347.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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