%I #17 Aug 16 2024 15:38:12

%S 1,4,36,1521,2325625,5408554896900,29252466072845872288372836,

%T 855706771342998810018458679815602502067088579902649,

%U 732234078522259249473123638277942895348884466303559008943210424176413224873174808848983192723595659649

%N a(n+1) = (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)=A143761(n), f(n,+1)=A143762(n),

%C f(n,-2)=A143763(n), f(n,+2)=a(n), f(n,-3)=A143765(n), f(n,+3)=A143766(n).

%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a> [_Reinhard Zumkeller_, Sep 11 2008]

%F a(n) ~ c^(2^n), where c = 1.581081999938782403516250856478461283288009405562783587423785805068844988... . - _Vaclav Kotesovec_, Dec 18 2014

%t s=1;lst={};Do[AppendTo[lst,s*=s+=n],{n,0,9}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 20 2009 *)

%t RecurrenceTable[{a[n+1] == (a[n]+n)^2, a[1] == 1}, a, {n, 1, 10}] (* _Vaclav Kotesovec_, Dec 18 2014 *)

%t FoldList[(#1+#2)^2&,1,Range@8] (* _Ivan N. Ianakiev_, May 08 2015 *)

%t nxt[{n_,a_}]:={n+1,(a+n)^2}; NestList[nxt,{1,1},10][[;;,2]] (* _Harvey P. Dale_, Aug 16 2024 *)

%Y Subsequence of A000290.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Sep 01 2008