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