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%I #18 May 09 2023 18:38:47
%S 1,48,1280,28672,589824,11534336,218103808,4026531840,73014444032,
%T 1305670057984,23089744183296,404620279021568,7036874417766400,
%U 121597189939003392,2089670227099910144,35740566642812256256,608742554432415203328,10330176681277348904960
%N a(n) = (2*n + 1)*16^n.
%H Vincenzo Librandi, <a href="/A165283/b165283.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (32,-256).
%F G.f.: (1+16*x)/(1-16*x)^2.
%F Sum_{n>=0} 1/a(n) = 2*log(5/3).
%F Sum_{n>=0} (-1)^n/a(n) = 4 * arctan(1/4). - _Amiram Eldar_, Jul 12 2020
%F E.g.f.: exp(16*x)*(1 + 32*x). - _Stefano Spezia_, May 09 2023
%o (PARI) a(n)=(2*n+1)*16^n
%o (Magma) [(2*n+1)*16^n: n in [0..20]]; // _Vincenzo Librandi_, Jun 08 2011
%Y Cf. A058962 ((2n+1)4^n), A155988 ((2n+1)9^n).
%K nonn,easy
%O 0,2
%A _Jaume Oliver Lafont_, Sep 13 2009
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