%I #28 Sep 08 2022 08:45:11
%S 1,4,18,76,312,1264,5088,20416,81792,327424,1310208,5241856,20969472,
%T 83881984,335536128,1342160896,5368676352,21474770944,85899214848,
%U 343597121536,1374389010432,5497557090304,21990230458368,87960926027776
%N Binomial transform of A081250.
%C When 5*2^n - 1 is prime, that is, n is in A001770, then a(n+1) is in A136539. - _Farideh Firoozbakht_ and _M. F. Hasler_, Nov 03 2012
%H Vincenzo Librandi, <a href="/A084213/b084213.txt">Table of n, a(n) for n = 0..400</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-8)
%F a(n) = (5*4^n - 2^(n+1) + 0^n)/4.
%F G.f.: (1 - 2*x + 2*x^2)/((1-2*x)*(1-4*x)).
%F E.g.f.: (5*exp(4*x) - 2*exp(2*x) + 1)/4.
%F a(n+1) = 2^n*(5*2^n - 1) for all n >= 0. - _M. F. Hasler_, Nov 03 2012
%p seq(coeff(series((1-2*x+2*x^2)/((1-2*x)*(1-4*x)),x,n+1), x, n), n = 0 .. 25); # _Muniru A Asiru_, Oct 09 2018
%t Table[If[n==0, 1, 2^(n-2)*(5*2^n - 2)], {n,0,30}] (* _G. C. Greubel_, Oct 08 2018 *)
%t CoefficientList[Series[(1 - 2*x + 2*x^2)/((1-2*x)*(1-4*x)), {x, 0, 50}], x] (* or *)
%t CoefficientList[Series[(5*Exp[4*x] - 2*Exp[2*x] + 1)/4, {x, 0, 50}], x]*Table[k!, {k, 0, 50}] (* _Stefano Spezia_, Oct 11 2018 *)
%o (Magma) [5*4^n/4-2^n/2+0^n/4: n in [0..30]]; // _Vincenzo Librandi_, Jun 15 2011
%o (PARI) vector(30, n, n--; (5*4^n - 2^(n+1) + 0^n)/4) \\ _G. C. Greubel_, Oct 08 2018
%K easy,nonn
%O 0,2
%A _Paul Barry_, May 19 2003