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 A186947 #28 Sep 15 2024 20:24:44
%S A186947 1,2,8,40,192,864,3712,15488,63488,257536,1038336,4171776,16728064,
%T A186947 67002368,268206080,1073250304,4293918720,17177640960,68714758144,
%U A186947 274867945472,1099490656256,4398002470912,17592093769728,70368551239680,281474574057472,1125899067981824
%N A186947 a(n) = 4^n - n*2^n.
%C A186947 Binomial transform of A186948.
%C A186947 Second binomial transform of A186949.
%H A186947 Harvey P. Dale, <a href="/A186947/b186947.txt">Table of n, a(n) for n = 0..1000</a>
%H A186947 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-20,16).
%F A186947 G.f.: (1 - 6*x + 12*x^2)/((1 - 2*x)^2*(1 - 4*x)).
%F A186947 a(n) = 4*a(n-1) + 2^n*(n-2), n >= 1. - _Vincenzo Librandi_, Mar 13 2011
%F A186947 a(n) = 2^n*A000325(n) = 4^n*A002064(-n) for all n in Z. - _Michael Somos_, Jul 18 2018
%F A186947 From _Elmo R. Oliveira_, Sep 15 2024: (Start)
%F A186947 E.g.f.: exp(2*x)*(exp(2*x) - 2*x).
%F A186947 a(n) = 8*a(n-1) - 20*a(n-2) + 16*a(n-3) for n > 2. (End)
%e A186947 G.f. = 1 + 2*x + 8*x^2 + 40*x^3 + 192*x^4 + 864*x^5 + 3712*x^6 + ... - _Michael Somos_, Jul 18 2018
%t A186947 Table[4^n-n 2^n,{n,0,30}] (* or *) LinearRecurrence[{8,-20,16},{1,2,8},30] (* _Harvey P. Dale_, Apr 23 2017 *)
%o A186947 (PARI) {a(n) = 2^n * (2^n - n)}; /* _Michael Somos_, Jul 18 2018 */
%o A186947 (Magma) [4^n - n*2^n: n in [0..30]]; // _G. C. Greubel_, Aug 14 2018
%Y A186947 Cf. A000325, A002064, A186948, A186949.
%K A186947 nonn,easy
%O A186947 0,2
%A A186947 _Paul Barry_, Mar 01 2011