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%I #8 Sep 11 2024 00:30:57
%S 1,55,349074740,7458911738724515315524082613205180,
%T 159232823342755035454279356693126603659457648808279391910878167820461916066223383414616137125812767424153893199341493609630
%N Sequence of iterated sums of squares (1^2+2^2+3^2+...+n^2).
%C 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.
%F 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))...))).
%e a(2)=T(T(2))=T(5)=55;
%e a(3)=T(T(T(3)))=T(T(14))=T(1015)=349074740.
%t t[n_]:=Sum[k^2,{k,n}];Table[Nest[t[#]&,n,n],{n,5}] (* _James C. McMahon_, Aug 10 2024 *)
%Y Cf. A000330, A099129.
%K nonn,easy
%O 1,2
%A _Hieronymus Fischer_, Jan 22 2006