|
%I #20 Sep 08 2022 08:44:35
%S 1,4,20,96,432,1856,7744,31744,128768,519168,2085888,8364032,33501184,
%T 134103040,536625152,2146959360,8588820480,34357379072,137433972736,
%U 549745328128,2199001235456,8796046884864,35184275619840,140737287028736,562949533990912
%N 2^n*(2^(n+1) - n - 1).
%H Vincenzo Librandi, <a href="/A008353/b008353.txt">Table of n, a(n) for n = 0..172</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-20,16).
%F a(n) = sum{k=0..n+1, C(2n+2, 2k)-2k(n-k+1)*C(n+1, k)/n}, n>0. - _Paul Barry_, Feb 24 2005
%F a(n) = 8*a(n-1)-20*a(n-2)+16*a(n-3). - _Colin Barker_, Feb 26 2015
%F G.f.: -(8*x^2-4*x+1) / ((2*x-1)^2*(4*x-1)). - _Colin Barker_, Feb 26 2015
%o (Magma) [2^n*(2^(n+1) - n - 1): n in [0..50]]; // _Vincenzo Librandi_, Apr 25 2011
%o (PARI) Vec(-(8*x^2-4*x+1)/((2*x-1)^2*(4*x-1)) + O(x^100)) \\ _Colin Barker_, Feb 26 2015
%Y a(n) = A066345(2*n+1).
%Y a(n) = 1 for n=0, 4 * A008464(n-2) else.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_ and _J. H. Conway_
|
