This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A166149 #22 Sep 08 2022 08:45:48 %S A166149 1,-5,35,-185,1235,-6785,43835,-247385,1562435,-8983985,55857035, %T A166149 -325376585,2001087635,-11762385185,71795014235,-424666569785, %U A166149 2578516996835,-15318514090385,92674023995435,-552229446706985 %N A166149 a(n) = (5^n + 10*(-6)^n)/11. %C A166149 From _Klaus Brockhaus_, Oct 14 2009: (Start) %C A166149 Fourth binomial transform of A014992. %C A166149 Sixth binomial transform is A001020 preceded by 1. %C A166149 Lim_{n -> infinity} a(n)/a(n-1) = -6. (End) %H A166149 Vincenzo Librandi, <a href="/A166149/b166149.txt">Table of n, a(n) for n = 0..200</a> %H A166149 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,30). %F A166149 a(n) = 30*a(n-2)-a(n-1), a(0)= 1, a(1)= -5. %F A166149 G.f.: (1-4x)/(1+x-30*x^2). %F A166149 a(n) = Sum_{k=0..n} A112555(n,k)*(-6)^k. %F A166149 E.g.f.: (1/11)*(exp(5*x) + 10*exp(-6*x)). - _G. C. Greubel_, May 01 2016 %t A166149 CoefficientList[Series[(1-4x)/(1+x-30x^2), {x,0,40}], x] (* _Harvey P. Dale_, Mar 11 2011 *) %t A166149 LinearRecurrence[{-1,30},{1,-5},20] (* _Harvey P. Dale_, Jan 20 2022 *) %o A166149 (Magma) [(5^n+10*(-6)^n)/11: n in [0..30]]; // _Vincenzo Librandi_, May 02 2011 %o A166149 (PARI) a(n)=(5^n+10*(-6)^n)/11 \\ _Charles R Greathouse IV_, May 02 2016 %Y A166149 Cf. A166035, A166036. %Y A166149 Cf. A014992 (q-integers for q=-10), A001020 (powers of 11). %K A166149 easy,sign %O A166149 0,2 %A A166149 _Philippe Deléham_, Oct 08 2009