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Inverse binomial transform of A026741.
1

%I #27 Sep 08 2022 08:45:48

%S 0,1,-1,3,-8,20,-48,112,-256,576,-1280,2816,-6144,13312,-28672,61440,

%T -131072,278528,-589824,1245184,-2621440,5505024,-11534336,24117248,

%U -50331648,104857600,-218103808,452984832,-939524096,1946157056,-4026531840,8321499136,-17179869184

%N Inverse binomial transform of A026741.

%H G. C. Greubel, <a href="/A168150/b168150.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-4,-4).

%F a(n+2) = (-1)^(n+1) * A001792(n).

%F From _R. J. Mathar_, Nov 23 2009: (Start)

%F a(n) = -4*a(n-1) -4*a(n-2) = (-2)^(n-3)*n, n>3.

%F G.f.: x*(1 + 3*x + 3*x^2)/(1 + 2*x)^2. (End)

%t Join[{0, 1, -1, 3}, LinearRecurrence[{-4, -4}, {-8, 20}, 50]] (* _G. C. Greubel_, Jul 14 2016 *)

%t CoefficientList[Series[x (1 + 3 x + 3 x^2) / (1 + 2 x)^2, {x, 0, 33}], x] (* _Vincenzo Librandi_, Jul 15 2016 *)

%o (PARI) a(n)=(-2)^if(n>1,n-3)*n \\ _M. F. Hasler_, Jan 25 2012

%o (Magma) [0,1] cat [(-2)^(n-3)*n: n in [2..35]]; // _Vincenzo Librandi_, Jul 15 2016

%Y Cf. A001792, A026741, A108189.

%K sign,easy

%O 0,4

%A _Paul Curtz_, Nov 19 2009

%E Comments turned into formulas, out-of-scope material moved to A026741 by _R. J. Mathar_, Nov 23 2009