OFFSET
1,2
COMMENTS
Can be understood as generalized iterated square pyramidal numbers. The growth of the sequence is bounded by O(n^3^n/3^(n/2)). This can be derived from the growth O(n^3/3) of the power two sum (1^2+2^2+3^2+...+n^2) by iteration.
FORMULA
Let T(n):=Sum_{k=1..n} k^2; we define a(1):=T(1), a(2):=T(T(2)) etc., a(n):=T(T(T(...T(n))...))).
EXAMPLE
a(2)=T(T(2))=T(5)=55;
a(3)=T(T(T(3)))=T(T(14))=T(1015)=349074740.
MATHEMATICA
t[n_]:=Sum[k^2, {k, n}]; Table[Nest[t[#]&, n, n], {n, 5}] (* James C. McMahon, Aug 10 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Hieronymus Fischer, Jan 22 2006
STATUS
approved