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 A097064 #22 Feb 13 2023 09:02:35
%S A097064 1,0,2,8,24,64,160,384,896,2048,4608,10240,22528,49152,106496,229376,
%T A097064 491520,1048576,2228224,4718592,9961472,20971520,44040192,92274688,
%U A097064 192937984,402653184,838860800,1744830464,3623878656,7516192768,15569256448,32212254720,66571993088
%N A097064 Expansion of (1 - 4*x + 6*x^2)/(1 - 2*x)^2.
%C A097064 Binomial transform of A097062.
%H A097064 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F A097064 a(n) = (n-1)*2^(n-1) + 3*0^n/2.
%F A097064 a(n) = 4*a(n-1) - 4*a(n-2), n>2.
%F A097064 a(n) = Sum_{k=0..n} binomial(n, k)*((2k-1)/2 + 3*(-1)^k/2).
%F A097064 a(n+1)/2 = A001787(n).
%F A097064 From _Amiram Eldar_, Oct 01 2022: (Start)
%F A097064 Sum_{n>=2} 1/a(n) = log(2) (A002162).
%F A097064 Sum_{n>=2} (-1)^n/a(n) = log(3/2) (A016578). (End)
%F A097064 E.g.f.: (3 - exp(2*x)*(1 - 2*x))/2. - _Stefano Spezia_, Feb 12 2023
%t A097064 CoefficientList[Series[(1-4x+6x^2)/(1-2x)^2,{x,0,30}],x] (* or *) Join[{1},LinearRecurrence[{4,-4},{0,2},30]] (* _Harvey P. Dale_, May 26 2011 *)
%Y A097064 Essentially the same as A036289.
%Y A097064 Cf. A001787, A002162, A016578, A097062.
%K A097064 easy,nonn
%O A097064 0,3
%A A097064 _Paul Barry_, Jul 22 2004