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%I #23 Dec 17 2014 11:59:26
%S 4,10,55,1540,1186570,703974775735,247790242435923759782980,
%T 30700002123226936025189367747945843590228731690,
%U 471245065183069190019624521318729501785547966685566656416776916445985874756815447988119493895
%N a(n+1) = a(n)*(a(n)+1)/2.
%H Reinhard Zumkeller, <a href="/A013589/b013589.txt">Table of n, a(n) for n = 0..11</a>
%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%F a(n) ~ 2 * c^(2^n), where c = 2.29524458756644851072790131811443639562180382439442714497... . - _Vaclav Kotesovec_, Dec 17 2014
%p f := proc(n) options remember; if n = 0 then 4 else 1/2*f(n-1)*(f(n-1)+1) fi end
%t a=4;lst={a};Do[b=(a+1)*a/2;AppendTo[lst,b];a=b,{n,1,9}];lst (* _Vladimir Joseph Stephan Orlovsky_, Mar 16 2010 *)
%t NestList[# (#+1)/2&,4,10] (* _Harvey P. Dale_, Sep 20 2012 *)
%o (Haskell)
%o a013589 n = a013589_list !! n
%o a013589_list = iterate a000217 4 -- _Reinhard Zumkeller_, Apr 10 2014
%Y Cf. A000217, A007501, A050542, A050536, A050548, A050909.
%Y Cf. A086714.
%K nonn
%O 0,1
%A Carl Bellinger (carlb(AT)ctron.com)
%E One more term from _Vladimir Joseph Stephan Orlovsky_, Mar 16 2010
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