A153061 a(-1) = 2, a(n) = a(n-1)^2 + n.

4, 17, 291, 84684, 7171379860, 51428689096413619605, 2644910062175573125355281735337640356031, 6995549236997594095768769895625713364190838574177475661857423797590740438072968

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Dec 17 2008

Keywords

• nonn

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..10
• Index entries for sequences of form a(n+1)=a(n)^2 + ...

Crossrefs

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

Programs

Mathematica

a=2;lst={};Do[a=a^2+n;AppendTo[lst,a],{n,0,10}];lst
RecurrenceTable[{a[0]==4,a[n]==a[n-1]^2+n},a,{n,10}] (* Harvey P. Dale, Oct 17 2013 *)

Python

def aupton(terms):
  alst = [4]
  for n in range(1, terms): alst.append(alst[-1]**2 + n)
  return alst
print(aupton(8)) # Michael S. Branicky, Apr 17 2021

Formula

a(n) ~ c^(2^n), where c = 4.1302388785110411646102486678455962713882427692215219090697122047307672779... . - Vaclav Kotesovec, Dec 18 2014