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%I #44 Oct 01 2022 06:09:09
%S 2,12,40,112,288,704,1664,3840,8704,19456,43008,94208,204800,442368,
%T 950272,2031616,4325376,9175040,19398656,40894464,85983232,180355072,
%U 377487360,788529152,1644167168,3422552064,7113539584,14763950080,30601641984,63350767616
%N a(n) = (2*n + 1) * 2^(n + 1).
%H Vincenzo Librandi, <a href="/A118417/b118417.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F a(n) = A118416(n+1,n) = 2*A014480(n).
%F G.f.: 2*(1-3*x^2+2*x^3)/((1-x)^2*(1-2*x)^2). - _Vincenzo Librandi_, Sep 02 2016
%F Sum_{n>=0} 1/a(n) = A196525. - _Fred Daniel Kline_, May 24 2019
%F Sum_{n>=0} (-1)^n/a(n) = arctan(1/sqrt(2))/sqrt(2) = A195695 / A002193. - _Amiram Eldar_, Oct 01 2022
%t CoefficientList[Series[2 (1 - 3 x^2 + 2 x^3)/((1 - x)^2 (1 - 2 x)^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Sep 02 2016 *)
%t Table[(2n+1)2^(n+1),{n,0,30}] (* or *) LinearRecurrence[{4,-4},{2,12},30] (* _Harvey P. Dale_, Oct 25 2021 *)
%o (Magma) [(2*n+1)*2^(n+1): n in [0..40]]; // _Vincenzo Librandi_, Dec 26 2010
%Y Cf. A014480, A118416.
%Y Cf. A002193, A196525, A195695.
%K nonn,easy
%O 0,1
%A _Reinhard Zumkeller_, Apr 27 2006
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