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 A100523 #15 Aug 17 2025 11:50:34
%S A100523 1,2,7,62,3967,15745022,247905749270527,61457260521381894004129398782,
%T A100523 3776994870793005510047522464634252677140721938309041881087
%N A100523 a(n) = a(n-1)^2 + 2*a(n-1) - 1 with a(0) = 1.
%H A100523 G. C. Greubel, <a href="/A100523/b100523.txt">Table of n, a(n) for n = 0..12</a>
%H A100523 <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1) = a(n)^2 + ...</a>
%F A100523 a(n) ~ c^(2^n), where c = 1.6784589651254290832096890907802189718037513767396728769965837700954845976... . - _Vaclav Kotesovec_, Dec 18 2014
%t A100523 RecurrenceTable[{a[n] == a[n-1]^2 + a[n-1]*2 - 1, a[0] == 1}, a, {n, 0, 10}] (* _Vaclav Kotesovec_, Dec 18 2014 *)
%t A100523 NestList[#^2+2#-1&,1,10] (* _Harvey P. Dale_, Aug 17 2025 *)
%o A100523 (Magma) [n le 1 select 1 else Self(n-1)^2 +2*Self(n-1) -1: n in [1..13]]; // _G. C. Greubel_, Jun 26 2022
%o A100523 (SageMath)
%o A100523 def a(n): return 1 if (n==0) else a(n-1)^2 + 2*a(n-1) - 1 # a=A100523
%o A100523 [a(n) for n in (0..12)] # _G. C. Greubel_, Jun 26 2022
%Y A100523 Cf. A004019.
%K A100523 nonn
%O A100523 0,2
%A A100523 _Reinhard Zumkeller_, Nov 24 2004