%I #13 Jun 27 2022 01:24:49
%S 1,2,7,62,3967,15745022,247905749270527,61457260521381894004129398782,
%T 3776994870793005510047522464634252677140721938309041881087
%N a(n) = a(n-1)^2 + 2*a(n-1) - 1 with a(0) = 1.
%H G. C. Greubel, <a href="/A100523/b100523.txt">Table of n, a(n) for n = 0..12</a>
%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1) = a(n)^2 + ...</a>
%F a(n) ~ c^(2^n), where c = 1.6784589651254290832096890907802189718037513767396728769965837700954845976... . - _Vaclav Kotesovec_, Dec 18 2014
%t RecurrenceTable[{a[n] == a[n-1]^2 + a[n-1]*2 - 1, a[0] == 1}, a, {n, 0, 10}] (* _Vaclav Kotesovec_, Dec 18 2014 *)
%o (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 (SageMath)
%o def a(n): return 1 if (n==0) else a(n-1)^2 + 2*a(n-1) - 1 # a=A100523
%o [a(n) for n in (0..12)] # _G. C. Greubel_, Jun 26 2022
%Y Cf. A004019.
%K nonn
%O 0,2
%A _Reinhard Zumkeller_, Nov 24 2004