%I #10 Oct 15 2017 12:08:30
%S 1,1,3,9,61,3441,11819871,139709267717593,
%T 19518679486184955909459972969,
%U 380978848884417414427615903969045678210740619589070918321
%N a(n+1) = a(n)^2 - n*a(n) + n^2, a(1) = 1.
%C Let f(n+1,k) = f(n,k)^2 + k*n*f(n,k) + n^2, f(1, k) = 1:
%C f(n,0)=A143760(n), f(n,-1)=a(n), f(n,+1)=A143762(n),
%C f(n,-2)=A143763(n), f(n,+2)=A143764(n), f(n,-3)=A143765(n),
%C f(n,+3)=A143766(n).
%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a> [From _Reinhard Zumkeller_, Sep 11 2008]
%F a(n) ~ c^(2^n), where c = 1.1356768837971801294990742257077941319336784846128736022759470343698650014... . - _Vaclav Kotesovec_, Dec 18 2014
%t RecurrenceTable[{a[n+1] == a[n]^2 - n*a[n] + n^2, a[1] == 1}, a, {n, 1, 10}] (* _Vaclav Kotesovec_, Dec 18 2014 *)
%t 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 *)
%K nonn
%O 1,3
%A _Reinhard Zumkeller_, Sep 01 2008