A143760 a(n+1) = a(n)^2 + n^2, a(1) = 1.

1, 2, 8, 73, 5345, 28569050, 816190617902536, 666167124752123519223995231345, 443778638100511299954105018279514127887014869775300070509089

Offset: 1

Author

Reinhard Zumkeller, Sep 01 2008

Keywords

• nonn

Comments

Let f(n+1,k) = f(n,k)^2 + k*n*f(n,k) + n^2, f(1, k) = 1:

f(n,0)=a(n), f(n,-1)=A143761(n), f(n,+1)=A143762(n),

f(n,-2)=A143763(n), f(n,+2)=A143764(n), f(n,-3)=A143765(n),

f(n,+3)=A143766(n).

Links

• Index entries for sequences of form a(n+1)=a(n)^2 + ... [From _Reinhard Zumkeller_, Sep 11 2008]

Programs

Mathematica

RecurrenceTable[{a[1]==1,a[n]==a[n-1]^2+(n-1)^2},a[n],{n,10}] (* Harvey P. Dale, May 03 2011 *)

Formula

a(n) ~ c^(2^n), where c = 1.3076706365483739101135324977730044318963776104568586126528165276768888613... . - Vaclav Kotesovec, Dec 18 2014