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 A128782 #24 May 13 2025 11:38:11
%S A128782 0,4,64,576,4096,25600,147456,802816,4194304,21233664,104857600,
%T A128782 507510784,2415919104,11341398016,52613349376,241591910400,
%U A128782 1099511627776,4964982194176,22265110462464,99230924406784,439804651110400,1939538511396864,8514618045497344,37225065669984256
%N A128782 a(n) = n^2*4^n.
%H A128782 Vincenzo Librandi, <a href="/A128782/b128782.txt">Table of n, a(n) for n = 0..1000</a>
%H A128782 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-48,64).
%F A128782 From _R. J. Mathar_, Sep 20 2011: (Start)
%F A128782 G.f.: 4*x*(1 + 4*x)/(1 - 4*x)^3 .
%F A128782 a(n) = 4*A086952(n). (End)
%F A128782 E.g.f.: 4*exp(4*x)*x*(1 + 4*x). - _Stefano Spezia_, Oct 09 2022
%t A128782 Table[n^2 * 4^n, {n, 0, 30}] (* _Vincenzo Librandi_, Feb 06 2013 *)
%t A128782 LinearRecurrence[{12,-48,64},{0,4,64},30] (* _Harvey P. Dale_, May 13 2025 *)
%o A128782 (Magma) [n^2*4^n: n in [0..20]]; // _Vincenzo Librandi_, Feb 06 2013
%Y A128782 Cf. A036289, A007758, A086952.
%K A128782 nonn,easy
%O A128782 0,2
%A A128782 _Mohammad K. Azarian_, Apr 07 2007