A153061 - OEIS

%I #20 Sep 06 2023 09:41:40

%S 4,17,291,84684,7171379860,51428689096413619605,

%T 2644910062175573125355281735337640356031,

%U 6995549236997594095768769895625713364190838574177475661857423797590740438072968

%N a(-1) = 2, a(n) = a(n-1)^2 + n.

%H Indranil Ghosh, <a href="/A153061/b153061.txt">Table of n, a(n) for n = 0..10</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 = 4.1302388785110411646102486678455962713882427692215219090697122047307672779... . - _Vaclav Kotesovec_, Dec 18 2014

%t a=2;lst={};Do[a=a^2+n;AppendTo[lst,a],{n,0,10}];lst

%t RecurrenceTable[{a[0]==4,a[n]==a[n-1]^2+n},a,{n,10}] (* _Harvey P. Dale_, Oct 17 2013 *)

%o (Python)

%o def aupton(terms):

%o   alst = [4]

%o   for n in range(1, terms): alst.append(alst[-1]**2 + n)

%o   return alst

%o print(aupton(8)) # _Michael S. Branicky_, Apr 17 2021

%Y Cf. A153059, A086851, A153060, A098152, A028300.

%K nonn

%O 0,1

%A _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008