A143761 a(n+1) = a(n)^2 - n*a(n) + n^2, a(1) = 1.

1, 1, 3, 9, 61, 3441, 11819871, 139709267717593, 19518679486184955909459972969, 380978848884417414427615903969045678210740619589070918321

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)=A143760(n), f(n,-1)=a(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[n+1] == a[n]^2 - n*a[n] + n^2, a[1] == 1}, a, {n, 1, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)
nxt[{n_,a_}]:={n+1,a^2-a(n+1)+(n+1)^2}; Join[{1},NestList[nxt,{1,1},10][[All,2]]] (* Harvey P. Dale, Oct 15 2017 *)

Formula

a(n) ~ c^(2^n), where c = 1.1356768837971801294990742257077941319336784846128736022759470343698650014... . - Vaclav Kotesovec, Dec 18 2014