This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A013589 #23 Dec 17 2014 11:59:26
%S A013589 4,10,55,1540,1186570,703974775735,247790242435923759782980,
%T A013589 30700002123226936025189367747945843590228731690,
%U A013589 471245065183069190019624521318729501785547966685566656416776916445985874756815447988119493895
%N A013589 a(n+1) = a(n)*(a(n)+1)/2.
%H A013589 Reinhard Zumkeller, <a href="/A013589/b013589.txt">Table of n, a(n) for n = 0..11</a>
%H A013589 <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%F A013589 a(n) ~ 2 * c^(2^n), where c = 2.29524458756644851072790131811443639562180382439442714497... . - _Vaclav Kotesovec_, Dec 17 2014
%p A013589 f := proc(n) options remember; if n = 0 then 4 else 1/2*f(n-1)*(f(n-1)+1) fi end
%t A013589 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 A013589 NestList[# (#+1)/2&,4,10] (* _Harvey P. Dale_, Sep 20 2012 *)
%o A013589 (Haskell)
%o A013589 a013589 n = a013589_list !! n
%o A013589 a013589_list = iterate a000217 4 -- _Reinhard Zumkeller_, Apr 10 2014
%Y A013589 Cf. A000217, A007501, A050542, A050536, A050548, A050909.
%Y A013589 Cf. A086714.
%K A013589 nonn
%O A013589 0,1
%A A013589 Carl Bellinger (carlb(AT)ctron.com)
%E A013589 One more term from _Vladimir Joseph Stephan Orlovsky_, Mar 16 2010