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A171501 Inverse binomial transform of A084640.

%I A171501 #23 Sep 08 2022 08:45:50
%S A171501 0,1,3,-1,7,-9,23,-41,87,-169,343,-681,1367,-2729,5463,-10921,21847,
%T A171501 -43689,87383,-174761,349527,-699049,1398103,-2796201,5592407,
%U A171501 -11184809,22369623,-44739241,89478487,-178956969,357913943,-715827881
%N A171501 Inverse binomial transform of A084640.
%C A171501 a(n) and differences are
%C A171501 0,     1,   3,  -1,    7,   -9,
%C A171501 1,     2,  -4,   8,  -16,   32,  =(-1)^(n+1) * A171449(n),
%C A171501 1,    -6,  12, -24,   48,  -96,
%C A171501 -7,   18, -36,  72, -144,  288,
%C A171501 25,  -54, 108, -216, 432, -864,
%C A171501 Vertical: 1) 0 followed with A168589(n).
%C A171501           2) (-1 followed with A008776(n) ) signed. See A025192(n).
%C A171501 Main diagonal: see A167747(1+n). - _Paul Curtz_, Jun 16 2011
%H A171501 Vincenzo Librandi, <a href="/A171501/b171501.txt">Table of n, a(n) for n = 0..1000</a>
%H A171501 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,2).
%F A171501 a(n) = A140966(n), n>0.
%F A171501 G.f.: x*(1+4*x) / ( (1+2*x)*(1-x) ). - _R. J. Mathar_, Jun 14 2011
%F A171501 a(1+n)= (-1)^(1+n) * A001045(1+n) + 2. - _Paul Curtz_, Jun 16 2011
%t A171501 CoefficientList[Series[x*(1 + 4*x)/((1 + 2*x)*(1 - x)), {x, 0, 30}], x]
%t A171501 LinearRecurrence[{-1,2},{0,1,3},40] (* _Harvey P. Dale_, Jan 14 2020 *)
%o A171501 (Magma) I:=[0, 1, 3]; [n le 3 select I[n] else -Self(n-1) + 2*Self(n-2): n in [1..40]]; // _Vincenzo Librandi_, Oct 18 2012
%K A171501 easy,sign
%O A171501 0,3
%A A171501 _Paul Curtz_, Dec 10 2009
%E A171501 Mathematica program by _Olivier Gérard_, Jul 06 2011