%I #22 Sep 08 2022 08:45:48

%S 1,-5,35,-185,1235,-6785,43835,-247385,1562435,-8983985,55857035,

%T -325376585,2001087635,-11762385185,71795014235,-424666569785,

%U 2578516996835,-15318514090385,92674023995435,-552229446706985

%N a(n) = (5^n + 10*(-6)^n)/11.

%C From _Klaus Brockhaus_, Oct 14 2009: (Start)

%C Fourth binomial transform of A014992.

%C Sixth binomial transform is A001020 preceded by 1.

%C Lim_{n -> infinity} a(n)/a(n-1) = -6. (End)

%H Vincenzo Librandi, <a href="/A166149/b166149.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,30).

%F a(n) = 30*a(n-2)-a(n-1), a(0)= 1, a(1)= -5.

%F G.f.: (1-4x)/(1+x-30*x^2).

%F a(n) = Sum_{k=0..n} A112555(n,k)*(-6)^k.

%F E.g.f.: (1/11)*(exp(5*x) + 10*exp(-6*x)). - _G. C. Greubel_, May 01 2016

%t CoefficientList[Series[(1-4x)/(1+x-30x^2), {x,0,40}], x] (* _Harvey P. Dale_, Mar 11 2011 *)

%t LinearRecurrence[{-1,30},{1,-5},20] (* _Harvey P. Dale_, Jan 20 2022 *)

%o (Magma) [(5^n+10*(-6)^n)/11: n in [0..30]]; // _Vincenzo Librandi_, May 02 2011

%o (PARI) a(n)=(5^n+10*(-6)^n)/11 \\ _Charles R Greathouse IV_, May 02 2016

%Y Cf. A166035, A166036.

%Y Cf. A014992 (q-integers for q=-10), A001020 (powers of 11).

%K easy,sign

%O 0,2

%A _Philippe Deléham_, Oct 08 2009