A115410 Sequence of iterated sums of squares (1^2+2^2+3^2+...+n^2).

1, 55, 349074740, 7458911738724515315524082613205180, 159232823342755035454279356693126603659457648808279391910878167820461916066223383414616137125812767424153893199341493609630

Offset: 1

Author

Hieronymus Fischer, Jan 22 2006

Keywords

• nonn
• easy

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.

Examples

			a(2) = T(T(2)) = T(5) = 55;
a(3) = T(T(T(3))) = T(T(14)) = T(1015) = 349074740.
		

Crossrefs

Cf. A000330, A099129.

Programs

Mathematica

t[n_]:=Sum[k^2,{k,n}];Table[Nest[t[#]&,n,n],{n,5}] (* James C. McMahon, Aug 10 2024 *)

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))...))).