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A141413 Inverse binomial transform of A140962.

%I A141413 #24 Mar 31 2021 01:28:16
%S A141413 0,-1,1,-3,9,-27,81,-243,729,-2187,6561,-19683,59049,-177147,531441,
%T A141413 -1594323,4782969,-14348907,43046721,-129140163,387420489,-1162261467,
%U A141413 3486784401,-10460353203,31381059609,-94143178827,282429536481,-847288609443
%N A141413 Inverse binomial transform of A140962.
%H A141413 Vincenzo Librandi, <a href="/A141413/b141413.txt">Table of n, a(n) for n = 0..1000</a>
%H A141413 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (-3).
%F A141413 a(n) = (-1)^n*A133494(n-1), n>0.
%F A141413 G.f.: (-x)*(1 + 2*x)/(1+3*x). - _R. J. Mathar_, Nov 11 2008
%F A141413 G.f.: x^2/( Q(0)+ 2*x)- x where Q(k) =  1 - x/(x*(k+1) - 1 )/Q(k+1) ; (recursively defined continued fraction). - _Sergei N. Gladkovskii_, Feb 24 2013
%F A141413 E.g.f.: (exp(-3*x) - (1 + 6*x))/9. - _Wolfdieter Lang_, Apr 19 2017
%F A141413 a(n) = (-3)^(n-2) for n >= 2, with a(0) = 0 and a(1) = -1. - _G. C. Greubel_, Mar 30 2021
%p A141413 A141413:= n-> `if`(n<2, -n, (-3)^(n-2)); seq(A141413(n), n=0..30); # _G. C. Greubel_, Mar 30 2021
%t A141413 CoefficientList[Series[-x(1+2x)/(1+3x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 24 2013 *)
%t A141413 Join[{0, -1},LinearRecurrence[{-3},{1},26]] (* _Ray Chandler_, Aug 12 2015 *)
%o A141413 (Magma) [0,-1] cat [(-3)^(n-2): n in [2..30]]; // _G. C. Greubel_, Mar 30 2021
%o A141413 (Sage) [-n if n<2 else (-3)^(n-2) for n in (0..30)] # _G. C. Greubel_, Mar 30 2021
%Y A141413 Cf. A285066 (alternating row sums, starting here with n >= 2). - _Wolfdieter Lang_, Apr 23 2017
%Y A141413 Cf. A000244, A133494.
%K A141413 sign,easy
%O A141413 0,4
%A A141413 _Paul Curtz_, Aug 04 2008
%E A141413 Edited and extended by _R. J. Mathar_, Nov 11 2008