cp's OEIS Frontend

A172160 a(0)=1. a(n) = 2^(n-2)*(5-n), for n>0.

%I A172160 #19 Apr 22 2022 17:55:20
%S A172160 1,2,3,4,4,0,-16,-64,-192,-512,-1280,-3072,-7168,-16384,-36864,-81920,
%T A172160 -180224,-393216,-851968,-1835008,-3932160,-8388608,-17825792,
%U A172160 -37748736,-79691776,-167772160,-352321536,-738197504,-1543503872,-3221225472,-6710886400
%N A172160 a(0)=1. a(n) = 2^(n-2)*(5-n), for n>0.
%C A172160 The inverse binomial transform is 1,1,0,0,-1,-1,-2,-2,-3,-3 = essentially A168050 or the negative of A004526.
%H A172160 Vincenzo Librandi, <a href="/A172160/b172160.txt">Table of n, a(n) for n = 0..1000</a>
%H A172160 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F A172160 a(n+1) - 2*a(n) = -A131577(n).
%F A172160 a(n) + A001787(n-1) = A000079(n+1).
%F A172160 a(n+5) = -A059165(n) = 4*A159964(n+1).
%F A172160 G.f.: (1 - 2*x - x^2)/(1-2*x)^2. - _R. J. Mathar_, Feb 11 2010
%F A172160 a(n) = 4*a(n-1) - 4*a(n-2), n>2.
%F A172160 E.g.f.: (1/4)*((5-2*x)*exp(2*x) - 1). - _G. C. Greubel_, Apr 21 2022
%F A172160 a(n) = 4^n*A045891(1-n) if n>1. - _Michael Somos_, Apr 22 2022
%e A172160 G.f. = 1 + 2*x + 3*x^2 + 4*x^3 + 4*x^4 - 16*x^6 - 64*x^7 + ... - _Michael Somos_, Apr 22 2022
%t A172160 Table[2^(n-2)*(5-n) -(1/4)*Boole[n==0], {n,0,40}] (* _G. C. Greubel_, Apr 21 2022 *)
%o A172160 (SageMath) [2^(n-2)*(5-n) -(1/4)*bool(n==0) for n in (1..40)] # _G. C. Greubel_, Apr 21 2022
%Y A172160 Cf. A004526, A045891, A168050.
%Y A172160 Cf. A000079, A001787, A059165, A159964, A131577.
%K A172160 sign,easy
%O A172160 0,2
%A A172160 _Paul Curtz_, Jan 27 2010
%E A172160 Definition replaced with closed form by _R. J. Mathar_, Feb 11 2010