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%I #46 Sep 08 2022 08:46:04
%S 2,4,16,128,2048,65536,4194304,536870912,137438953472,70368744177664,
%T 72057594037927936,147573952589676412928,604462909807314587353088
%N a(n) = 2^((2 + n + n^2)/2).
%H Vincenzo Librandi, <a href="/A217994/b217994.txt">Table of n, a(n) for n = 0..80</a>
%F a(n) = a(n-1)*(2^n), with a(0)=2.
%F G.f.: G(0)/x -1/x, where G(k)= 1 + 2^k*x/(1 - x/(x + x/G(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Jul 26 2013
%e a(3) = 128 because a(3) = 2^(2 + 3 + 3^2)/2 = 2^14/2 = 2^7 = 128.
%t Table[2^((2 + n + n^2) / 2), {n, 0, 30}] (* _Vincenzo Librandi_, Jul 26 2013 *)
%o (Maxima) A217994[n]:=2^((2+n+n^2)/2)$
%o makelist(A217994[n],n,0,30); /* _Martin Ettl_, Oct 29 2012 */
%o (PARI) a(n)=2<<((n+n^2)/2) \\ _Charles R Greathouse IV_, Jan 06 2013
%o (Magma) [2^((2 + n + n^2) div 2): n in [0..15]]; // _Vincenzo Librandi_, Jul 26 2013
%K nonn,easy
%O 0,1
%A _Mokhtar Mohamed_, Oct 19 2012