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%I #40 Feb 07 2024 12:29:40
%S 1,-8,73,-656,5905,-53144,478297,-4304672,38742049,-348678440,
%T 3138105961,-28242953648,254186582833,-2287679245496,20589113209465,
%U -185302018885184,1667718169966657,-15009463529699912
%N a(n) = (1 - (-9)^n)/10.
%C q-integers for q = -9.
%H Vincenzo Librandi, <a href="/A014991/b014991.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-8,9).
%F a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1).
%F a(0)=1, a(1)=-8, a(n) = -8*a(n-1) + 9*a(n-2). - _Harvey P. Dale_, Aug 08 2011
%F G.f.: x/((1 - x)*(1 + 9*x)). - _Vincenzo Librandi_, Oct 22 2012
%F E.g.f.: (exp(x) - exp(-9*x))/10. - _G. C. Greubel_, May 26 2018
%p a:=n->sum ((-9)^j, j=0..n): seq(a(n), n=0..25); # _Zerinvary Lajos_, Dec 16 2008
%t ((-9)^Range[30]-1)/-10 (* or *) LinearRecurrence[{-8,9},{1,-8},30] (* _Harvey P. Dale_, Aug 08 2011 *)
%t CoefficientList[Series[1/((1 - x)*(1 + 9*x)), {x, 0, 30}], x]; (* _Vincenzo Librandi_, Oct 22 2012 *)
%o (Sage) [gaussian_binomial(n,1,-9) for n in range(1,19)] # _Zerinvary Lajos_, May 28 2009
%o (Magma) I:=[1,-8]; [n le 2 select I[n] else -8*Self(n-1)+9*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Oct 22 2012
%o (PARI) for(n=1,30, print1((1-(-9)^n)/10, ", ")) \\ _G. C. Greubel_, May 26 2018
%Y Cf. A077925, A014983, A014985-A014987, A014989-A014994. - _Zerinvary Lajos_, Dec 16 2008
%K sign,easy
%O 1,2
%A _Olivier Gérard_
%E Better name from _Ralf Stephan_, Jul 14 2013
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