%I A115410
%S A115410 1,55,349074740,7458911738724515315524082613205180,
%T A115410 1592328233427550354542793566931266036594576488082793919108781678204619160662233834146161371258127674241538931\
               99341493609630
%N A115410 Sequence of iterated sums of squares (1^2+2^2+3^2+...+n^2).
%C A115410 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 A115410 Let T(n):=sum{k^2|k=1...n}; we define a(1):=T(1), a(2):=T(T(2)) etc., 
               a(n):=T(T(T(...T(n))...))).
%e A115410 a(2)=T(T(2))=T(5)=55;
%e A115410 a(3)=T(T(T(3)))=T(T(14)=T(1015)=349074740.
%Y A115410 Cf. A000330, A099129.
%Y A115410 Sequence in context: A027580 A046194 A093255 this_sequence A036197 A107676 
               A005932
%Y A115410 Adjacent sequences: A115407 A115408 A115409 this_sequence A115411 A115412 
               A115413
%K A115410 nonn
%O A115410 1,2
%A A115410 Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jan 22 2006