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%I #9 Sep 25 2021 02:00:10
%S 1,2,4,6,8,12,20,52,308,8500,2105652,17181974836,36028814200938804,
%T 618970019678718951650500916,
%U 22300745198530623760505737951367313156481332
%N Nonlinear recursion: a(n) = a(n-1) + Product_{i=1..(n-1)/2} a(n-2i+1)-a(n-2i).
%C Initial conditions: a(1)=1; a(2)=1; a(3)=4;
%C With a(3)=3, the recursion gives the positive integers.
%t a[1]:= 1; a[2]:= 2; a[3]:= 4;
%t a[n_Integer]:=a[n]=a[n-1]+ Times@@Table[(a[n-2i+1]-a[n-2i]),{i,1,(n-1)/2}];
%t Table[a[n],{n,1,15}]
%K nonn,easy
%O 1,2
%A _Olivier Gérard_, Aug 24 2013
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