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%I
%S 1,2,40,320,21504,688128,178257920,22817013760,23433341566976,
%T 11997870882291712,49179307930885816320,100719222642454151823360,
%U 1650485975228872480767606784,13520781109074923362448234774528
%N The "Fi1" sums of the powers-of-2 triangle A000079
%C The a(n) represent the Fi1(n) sums, see A180662, of the powers-of-2 triangle A000079. We observe that Fi2(2*n) = Fi1(2*n) and Fi2(2*n+1) = 2*Fi1(2*n+1).
%F a(2*n+1) = 2^(2*n+1)*a(2*n) and a(2*n+2) = 2^(2*n+2)*((4^(n+2) - 1)/(4^(n+1) - 1))*a(2*n+1) with a(0) = 1 and a(1) =2.
%p nmax:=13: a(0):=1: a(1):=2: for n from 0 to nmax/2 do a(2*n+1):= 2^(2*n+1)*a(2*n): a(2*n+2):=2^(2*n+2)*((4^(n+2) - 1)/(4^(n+1) - 1))*a(2*n+1): od: seq(a(n),n=0..nmax);
%K easy,nonn
%O 0,2
%A _Johannes W. Meijer_, Oct 10 2010
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