A143764 a(n+1) = (a(n)+n)^2, a(1) = 1.

1, 4, 36, 1521, 2325625, 5408554896900, 29252466072845872288372836, 855706771342998810018458679815602502067088579902649, 732234078522259249473123638277942895348884466303559008943210424176413224873174808848983192723595659649

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)=A143761(n), f(n,+1)=A143762(n),

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

Links

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

Crossrefs

Subsequence of A000290.

Programs

Mathematica

s=1;lst={};Do[AppendTo[lst,s*=s+=n],{n,0,9}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 20 2009 *)
RecurrenceTable[{a[n+1] == (a[n]+n)^2, a[1] == 1}, a, {n, 1, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)
FoldList[(#1+#2)^2&,1,Range@8] (* Ivan N. Ianakiev, May 08 2015 *)
nxt[{n_,a_}]:={n+1,(a+n)^2}; NestList[nxt,{1,1},10][[;;,2]] (* Harvey P. Dale, Aug 16 2024 *)

Formula

a(n) ~ c^(2^n), where c = 1.581081999938782403516250856478461283288009405562783587423785805068844988... . - Vaclav Kotesovec, Dec 18 2014