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